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aqua_rat__rCvones6PfUnselb

In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl? Pick A) 110 B) 120 C) 130 D) 195 E) 200

The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are: (i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1 x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1= <gadget id="calculator">80 + 90 + 24 + 1</gadget> <output>195</output> 195 195 <result>D</result>

D

In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?

aqua_rat__v6FOqGnvfSXtnbsX

In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr? Choose the correct choice from the following options: A) 2.5 sec B) 1.9 sec C) 8.9 sec D) 6.9 sec E) 5 sec

Speed = 144 * 5/18= <gadget id="calculator">144 * 5/18</gadget> <output>40</output> 40 m/sec Time taken= 200/40= <gadget id="calculator">200/40</gadget> <output>5</output> 5 sec. Answer: 5 sec <result>E</result>

E

In what time will a train 200 m long cross an electric pole, it its speed be 144 km/hr?

aqua_rat__b5OfMxWjwLNCudwb

The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 231 the Other is Choices: A) 330 B) 300 C) 270 D) 250 E) 350

The other number = L.C.M * H.C.F/given number = 2310*30/231= <gadget id="calculator">2310*30/231</gadget> <output>300</output> 300 Answer is 300. <result>B</result>

B

The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 231 the Other is

aqua_rat__ahUziAyKkKCXyQfP

In an examination, a student scores 3 marks for every correct answer and loses 2 marks for every wrong answer. If he attempts all 100 questions and secures 300 marks, the number of questions he attempts correctly, is: Answers: A) 150 B) 250 C) 400 D) 300 E) 100

Let the number of correct answers be x. Number of incorrect answers = (100 – x). 3x – 2(100 – x) = 300 or 5x = 500 or x = 100. ANSW100R:100 <result>E</result>

E

In an examination, a student scores 3 marks for every correct answer and loses 2 marks for every wrong answer. If he attempts all 100 questions and secures 300 marks, the number of questions he attempts correctly, is:

aqua_rat__RQbrEPIf55ycpJTg

An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m? Select the correct option A) Rs. 3642.40 B) Rs. 3868.80 C) Rs. 4216.20 D) Rs. 4082.40 E) None of these

Length of the first carpet = (1.44)(6) = 8.64 cm Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100) = 51.84(1.4)(5/4) sq m = (12.96)(7) sq m Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40 ANSWER:Rs. 4082.40 <result>D</result>

D

An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?

aqua_rat__srBJ9amIP7uaKyxW

Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 20 km/hr and 30 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions? Choose one: A) 28 sec B) 37 sec C) 21.6 sec D) 23 sec E) 27 sec

Time taken to meet for the first time anywhere on the track = length of the track / relative speed = 400 / (20 + 30)5/18 = 300* 18 / 50 * 5 = 21.6 seconds. Answer : 21.6 sec <result>C</result>

C

Two persons start running simultaneously around a circular track of length 400 m from the same point at speeds of 20 km/hr and 30 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?

aqua_rat__ibSXXtnxL875sJBO

405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive? Choose the correct choice from the following options: A) 7 B) 9 C) 18 D) 45 E) None of these

Let the total number of children be x. Then, x × (20 % of x) = 405 ⇔ 1⁄5 x2 = 405 ⇔ x2 = 2025 ⇔ x = 45 ∴ Number of sweets received by each child = 20% of 45 = 9 Answer 9 <result>B</result>

B

405 sweets were distributed equally among children in such a way that the number of sweets received by each child is 20% of the total number of children. How many sweets did each child receive?

aqua_rat__52e3vsFDmpeSMJ9U

In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true? I) k=0 II) k=−1 III) k=−3 Choices A) I only B) III only C) I and II only D) II and III only E) I and III only

Please format the question properly. Per the question, x^2+kx+1=0 with k=constant. For a quadratic equation (ax2+bx+c=0) to have 2 distinct roots ---&gt; D=b2−4ac&gt;0 ---&gt; k^2−4&gt;0 ---&gt;k&lt;−2or k&gt;2 . Only III falls in these ranges. III only is the correct answer. <result>B</result>

B

In the equation x^2+kx+1=0, x is a variable and k is a constant. If the quadratic equation has two distinct real roots, which of the following could be true? I) k=0 II) k=−1 III) k=−3

aqua_rat__rpifQmnKXce4EtHB

When 200 is divided by positive integer x, the remainder is 2. What is the remainder when 398 is divided by x? Choose one. A) 2 B) 3 C) 4 D) 6 E) 8

f200/x leaves a reminder 2 then (200-2) i.e. 198 is divisible by x So (200+198)/x leaves a reminder rem(200/x)+rem(198/x)=&gt; 2+0= <gadget id="calculator">2+0</gadget> <output>2</output> 2 2nswer :2 <result>A</result>

A

When 200 is divided by positive integer x, the remainder is 2. What is the remainder when 398 is divided by x?

aqua_rat__iZleW21JycTZp0YP

A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.5 per box per month for the record storage, what is the total amount that the company pays each month for record storage? Choose the correct choice from the following options. A) a. 150 B) b. 300 C) c. 600 D) d. 1,200 E) e. 2,400

Volume Per b. 300ox: 15x12x10 = 1,800 Total Volume: 1,080,000 Number of b. 300oxes: Total Volume / Volume Per b. 300ox = 1,080,000 / 1,800 = 600 Price Per Month: Number of b. 300oxes * Price Per b. 300ox = 600 * 0.5= <gadget id="calculator">600 * 0.5</gadget> <output>300</output> 300 Answer: b. 300 <result>B</result>

B

A certain company has records stored with a record storage firm in 15-inch by 12-inch by 10-inch boxes. The boxes occupy 1.08 million cubic inches of space. If the company pays $0.5 per box per month for the record storage, what is the total amount that the company pays each month for record storage?

aqua_rat__DAKheENrWkbsadEf

A group of students was interviewed for that if it was asked whether or not they speak Spanish and / or English. Among those who speak Spanish, 15 speak English well, while 45 of them do not speak English. If 70% of students do not speak Spanish, how many students were surveyed? Choose the correct choice from the following answers A) 200 B) 220 C) 230 D) 210 E) 215

Number of students who speak Spanish are 45 + 15= <gadget id="calculator">45 + 15</gadget> <output>60</output> 60 Of total students, the percentage of students who do not speak Spanish was 70% --&gt; percentage of who do is 30% 60-------30% x ------- 100% x= 60*100/30= <gadget id="calculator">60*100/30</gadget> <output>200</output> 200= number of all students 200nswer is 200 <result>A</result>

A

A group of students was interviewed for that if it was asked whether or not they speak Spanish and / or English. Among those who speak Spanish, 15 speak English well, while 45 of them do not speak English. If 70% of students do not speak Spanish, how many students were surveyed?

aqua_rat__WBz5hgiHIv14LrTb

Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 2 hours? Choose the correct choice from the following answers. A) 2.4. B) 3.2. C) 4.2. D) 5.5. E) 6.4

W = 2 desks T = 2.5 hrs Rate of 2 carpenters = 2×R Rate = work done/ time 2xR = 2/2.5 R = 1/2.5 = 2/5 (this is the rate of each carpenter) Work done by 4 carpenters in 2 hrs = 4 × rate of each carpenter x time = 4× 2/5 × 2 = 3.2 desks 3.2. is the correct answer. <result>B</result>

B

Two carpenters, working in the same pace, can build 2 desks in two hours and a half. How many desks can 4 carpenters build in 2 hours?

aqua_rat__w9EdDua91BUzK6XE

Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 6 years? Select A) 5x (1+n/100)^5 - x B) 6x (1+n/100)^4 - x C) x (1+n/100)^6 - x D) 2x (1+n/100)^7 - x E) 4x (1+n/100)^8 - x

Amount after 6 years compounded yearly = x (1+n/100)^6 Thus profit = Final amount - original principle = x (1+n/100)^6 - x . Answer : x (1+n/100)^6 - x <result>C</result>

C

Which of the following represents the profit from the investment of x dollars at n percent compound annual interest for 6 years?

aqua_rat__jwWRIz4z6Qz0y9Wb

If 140/x is an integer and 108/x is an integer, which of the following must be true? I. 9/x is an integer II. 12/x is an integer III. 36/x is an integer Choose the correct choice from the following A) I only B) III only C) I and II only D) II and III only E) I, II and III

I think, here we should use the greatest common factor. The greatest common factor for 144 and 108 is 36. So 36/x is an integer. For the rest of the answers, if x is 36 then 9/x and 12/x leads to fractions. Ans is I, II and III. <result>E</result>

E

If 140/x is an integer and 108/x is an integer, which of the following must be true? I. 9/x is an integer II. 12/x is an integer III. 36/x is an integer

aqua_rat__LjSdK5tM3QnBs3GJ

The current in a river is 6 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours? Choose the correct choice from the following A) 69 miles B) 88 miles C) 96 miles D) 91 miles E) 112 miles

Upstream Speed = 20-6= <gadget id="calculator">20-6</gadget> <output>14</output> 14 mph 91 milesownstream Speed= 20+6= <gadget id="calculator">20+6</gadget> <output>26</output> 26 mph 91 miles/14 + 91 miles/26= 10 hours Solving for 91 miles we get 91 miles=91 Answer: 91 miles <result>D</result>

D

The current in a river is 6 mph. A boat can travel 20 mph in still water. How far up the river can the boat travel if the round trip is to take 10 hours?

aqua_rat__RJdnrLBARFkbONi5

How many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards? (1 mile = 1,160 yards) Choose one. A) 2 B) 5 C) 4 D) 3.61 E) 4.3

speed = 9 miles/hr = 4.4 yard/s = 29.33 yards/min distance = 106 yards time = distance/speed =106/29.33 =3.61 minutes ans - 3.61 <result>D</result>

D

How many minutes will it take for a car that is traveling at a constant rate of 9 miles per hour to travel a distance of 106 yards? (1 mile = 1,160 yards)

aqua_rat__07lfUbBehOGFnjlf

A train passes a station platform in 30 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? Choose one: A) 200 B) 220 C) 240 D) 150 E) 260

Speed = [54 * 5/18] m/sec = 15 m/sec. Length of the train = (15 * 20)= <gadget id="calculator">(15 * 20)</gadget> <output>300</output> 300 m. Let the length of the platform be x meters. Then, x + 300 / 30= 15 x + 300 = 450 x = 150 m. Answer: Option 150 <result>D</result>

D

A train passes a station platform in 30 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?

aqua_rat__Ss2szK50iqwAfW8t

Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle? Choose the correct choice A) 120 B) 150 C) 200 D) 270 E) 420

To make a triangle, you need 2 checkpoints from one track and 1 from the other. You cannot have all 3 from the same track since then the points will be in a line (assuming straight line of track) You select 2 checkpoints from the first track and one from the second or two from the second track and one from the first. 6C2 * 10C1 + 10C2 * 6C1 = 150 + 270= <gadget id="calculator">150 + 270</gadget> <output>420</output> 420 Answer (420) <result>E</result>

E

Two tracks are parallel. The first track has 6 checkpoints and the second one has 10 checkpoints. In how many ways can the 6 checkpoints of first track be joined with the 10 checkpoints of the second to form a triangle?

aqua_rat__UYvA75wDl5EM7VHe

Seller selling an apple for Rs.20, a Seller loses 1/6th of what it costs him. The CP of the apple is? Select the correct option: A) 10 B) 12 C) 21 D) 18 E) 20

SP=20Loss=21P21Loss=21P−SP=21P−20⇒21P21=21P−20⇒20 21P21=20⇒21P21=1⇒21P=21 21 <result>C</result>

C

Seller selling an apple for Rs.20, a Seller loses 1/6th of what it costs him. The CP of the apple is?

aqua_rat__Hdrv74rkqofyRjci

Sixty five percent of a number is 21 less than four fifth of that number. What is the number ? Pick one: A) 240 B) 140 C) 230 D) 130 E) 125

Let the number be x. Then, 4*x/5 –(65% of x) = 21 4x/5 – 65x/100 = 21 5x = 2100 x = 140. Answer 140. <result>B</result>

B

Sixty five percent of a number is 21 less than four fifth of that number. What is the number ?

aqua_rat__TkoQ6wxE2ssueVkY

4.509/10.02 = Choose one: A) 0.45 B) 0.3505 C) 0.3509 D) 0.351 E) 0.3527

4.509 / 10.02 4509 / 1002= <gadget id="calculator">4509 / 1002</gadget> <output>9/2 = around 4.5</output> 4.5 move the comma two places to the left as we have 2 decimal places from the divisor: 0.45. 0.45nswer: 0.45 <result>A</result>

A

4.509/10.02 =

aqua_rat__jaRaNuZZF4dlwcKu

An 80-liter solution of cool-drink is made from 10% jasmine water. If 8 liters of jasmine and 12 liters of water were added to the solution, what percent of the solution is jasmine? Choices. A) 12% B) 14% C) 16% D) 18% E) 20%

The percent of jasmine in the resulting solution is: (amount of jasmine) / (total volume) (0.1(80) + 8) / 100 = 16/100 = 16% The answer is 16%. <result>C</result>

C

An 80-liter solution of cool-drink is made from 10% jasmine water. If 8 liters of jasmine and 12 liters of water were added to the solution, what percent of the solution is jasmine?

aqua_rat__fBcpMejbeATHogp1

The ratio of two numbers is 2 : 3 and their H.C.F. is 6. Their L.C.M. is Choose the correct choice from the following choices: A) 48 B) 22 C) 36 D) 27 E) 67

Explanation: Let the numbers be 2x and 3x. Then, their H.C.F. = x. So, x = 6. So, the numbers 12 and 18 L.C.M. of 12 and 18 = 36 Option 36 <result>C</result>

C

The ratio of two numbers is 2 : 3 and their H.C.F. is 6. Their L.C.M. is

aqua_rat__8jQY2y0HyTvAlJtC

A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream? Choose the correct choice from the following choices. A) 30/83 hours B) 80/13 hours C) 30/19 hours D) 30/13 hours E) 31/13 hours

Speed downstream = 20 + 6= <gadget id="calculator">20 + 6</gadget> <output>26</output> 26 kmph. Time required to cover 60 km downstream= d/s = 60/26 = 30/13 hours. Answer: 30/13 hours <result>D</result>

D

A man can row a boat at 20 kmph in still water. If the speed of the stream is 6 kmph, what is the time taken to row a distance of 60 km downstream?

aqua_rat__aXze5FgIpee0iPVc

In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit? Choose the correct choice from the following choices: A) 200 % B) 75 % C) 150 % D) 50 % E) 70%

Explanation: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420. New C.P. = 125% of Rs. 100 = Rs. 125 New S.P. = Rs. 420. Profit = Rs. (420 - 125) = Rs. 295 Required percentage =(295/420*100)%=1475/21%=70% Answer:70% <result>E</result>

E

In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?

aqua_rat__XAisKUjc2Xf4kj5O

If the sum of the first n positive integers is x, then which of the following is the sum of the first 2n even positive integers? Choose the correct option: A) 2x + 2n^2 B) 3x + 4n^2 C) 4x + 2n D) 4x + n^2 E) 4x + 2n^2

n(n+1)/2 = x or n^2 + n = 2x (1) If the series has first 2n numbers, sum of n odd numbers = n^2. So sum of n even numbers= Sum of first 2n numbers - n^2 In this case we have 2n even numbers so 2n odd numbers will be there, hence a total of 4n first numbers. Sum of first 4n numbers = 4n(4n+1)/2 -----------(2) Sum of first 2n odd numbers is (2n)^2 = 4n^2 ---------------- (3) So sum of 2n even numbers is (2)-(3) or 4n^2+2n or 2n^2 + 2 (n^2+n) or 2n^2 + 2(2x) or 2n^2 + 4x ANSW4x + 2n^2R:4x + 2n^2 <result>E</result>

E

If the sum of the first n positive integers is x, then which of the following is the sum of the first 2n even positive integers?

aqua_rat__c5tR8GoDqnqjAkR3

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? Answers. A) 7 B) 8.2 C) 2 D) 10.8 E) 11.2

Answer: Option D Relative speed = 60 + 40= <gadget id="calculator">60 + 40</gadget> <output>100</output> 100 km/hr.= 100 * 5/18 = 250/9 m/sec. Distance covered in crossing each other = 140 + 160= <gadget id="calculator">140 + 160</gadget> <output>300</output> 300 m. Required time= 300 * 9/250 = 54/5= <gadget id="calculator">54/5</gadget> <output>54/5 = around 10.8</output> 10.8 sec <result>D</result>

D

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?

aqua_rat__PrFHyJfN6U6zXq39

A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone. Choose one. A) 6 ½ days B) 1 ½ days C) 8 ½ days D) 5 ½ days E) 2 ½ days

Explanation: 3/20 * 2 + (2 + x)/5 = 1 x = 1 ½ days Answer:1 ½ days <result>B</result>

B

A and B can do a piece of work in 6 2/3 days and 5 days respectively. They work together for 2 days and then A leaves. In how many days after that B will complete the work alone.

aqua_rat__xpDhrC5g1mirRDiU

If x ≠ 0 and x - (2- x^2)/x = y/x, then y = Choose one. A) − 2 − 3x^2 B) x^2 − 2 C) 2x^2 − 2 D) x − 2 − x^2 E) x − 2 + x^2

We're told that x ≠ 0 and x - (2- x^2)/x = y/x. We're asked for the value of y. IF.... X = 3 3 - (2 - 3^2)/3 = y/3 9/3 - (-7/3) = y/3 Multiply everything by 3.... 9 - (-7)= <gadget id="calculator">9 - (-7)</gadget> <output>16</output> y 16= y So we're looking for an answer that equals 16 when x = 3... Answer A) − 2 − 3x^2 This will be NEGATIVE, so no need to calculate it. Answer B) x^2 − 2 = 7. NOT a match. Answer C) 2x^2 − 2 = 16. This IS a match. Answer D) x − 2 − x^2 This will be NEGATIVE, so no need to calculate it. Answer E) x − 2 + x^2 = 10. NOT a match. Final Answer:2x^2 − 2 <result>C</result>

C

If x ≠ 0 and x - (2- x^2)/x = y/x, then y =

aqua_rat__X2ZRl7h3l9YMa4X5

If takes 25.5 minutes to download a file using Modem A. Modem B work at 17% of the speed of Modem A. How long does it take to download a file using a Modem B? Choices. A) 130 minutes B) 140 minutes C) 150 minutes D) 160 minutes E) 170 minutes

Let Speed of modem A be k So Speed of modem B is 17/100*k Time taken by modem A = 25.5 minutes Let time taken by modem B = x k*25.5 = 17/100*k*x 0.17*x = 25.5 x = 25.5/0.17= <gadget id="calculator">25.5/0.17</gadget> <output>150</output> 150 minutes ANSWER:150 minutes <result>C</result>

C

If takes 25.5 minutes to download a file using Modem A. Modem B work at 17% of the speed of Modem A. How long does it take to download a file using a Modem B?

aqua_rat__QcvdG6PhNod1BER6

If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage? Choose the correct choice from the following A) 50% B) 100% C) 45% D) 55% E) 65%

Let the C.P of each book be Re 1. Then, S.P of 5 books= C.P of 10 books= Rs. 10 Now, C.P of 5 books= Rs.5, S.p of 5 books= Rs 10 Gain = Rs ( 10 -5 )= <gadget id="calculator">( 10 -5 )</gadget> <output>5</output> Rs 5. Gain%= ( 5/5× 100 ) % = 100% Answer : 100% <result>B</result>

B

If the selling price of 5 books is same as the cost price of 10 books. Find the gain or loss percentage?

aqua_rat__1Hcw65gTfYSYewU2

Two trains of equal length, running with the speeds of 50 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions? Pick: A) 5.55 sec B) 4.55 sec C) 5.95 sec D) 6.55 sec E) 9.55 sec

RS = 50 -40= <gadget id="calculator">50 -40</gadget> <output>10</output> 10 * 5/18= 50/18 T = 50 D = 50 * 50/18 = 1250/9 RS = 50 + 40= <gadget id="calculator">50 + 40</gadget> <output>90</output> 90 * 5/18= <gadget id="calculator">90 * 5/18</gadget> <output>25</output> 25 T= 1250/9 * 1/25 = 5.55 sec 5.55 secNSWER:5.55 sec <result>A</result>

A

Two trains of equal length, running with the speeds of 50 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions?

aqua_rat__gt0x5bUEPccQkyW0

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is: Choose the correct choice from the following: A) 22 B) 28 C) 32 D) 48 E) 92

Let the son's present age be x years. Then, man's present age = (x + 24) years. (x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 =&gt; x = 22. answer is 22. <result>A</result>

A

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is:

aqua_rat__dolbTs43ogRbxrH6

if b is a positive integer greater than 8, which of the following must be divisible by 4? Choose the most appropriate option: A) b(b-1)(b+2)(b+3) B) b(b-1)(b+3)(b+4) C) b(b-3)(b+2)(b+4) D) b(b-3)(b+2)(b+3) E) b(b+1)(b+3)(b+4)

D. For any integer b, D is the only answer choice which will always be divisible by 4. A product of 4 consecutive integers will always be divisible by 4. Since, none of the answer choices are a product of 4 consecutive integers, we have to ensure at least one of the integers is always a multiple of 4. The best way to do that is to ensure the answer choice isb* [(b-1)OR(b+3)] * [(b-2)OR(b+2)] * [(b-3)OR(b+1)]. (answer b(b-3)(b+2)(b+3)) <result>D</result>

D

if b is a positive integer greater than 8, which of the following must be divisible by 4?

aqua_rat__Lq0nGFcIOqMLNFvh

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is: Select A) 44% B) 46% C) 48% D) 50% E) 51%

Let original length = x metres and original breadth = y metres. Original area = (xy) m2. New length = 120 x m = 6 x m. 100 5 New breadth = 120 y m = 6 y m. 100 5 New Area = 6 x x 6 y m2 = 36 xy m2. 5 5 25 The difference between the original area = xy and new-area 36/25 xy is = (36/25)xy - xy = xy(36/25 - 1) = xy(11/25) or (11/25)xy Increase % = 11 xy x 1 x 100 % = 44%. 25 xy 44% <result>A</result>

A

The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:

aqua_rat__yOOQgXgtxkgDwqX2

3,9,27,81,.... Choose one A) 583 B) 604 C) 616 D) 243 E) 636

1*3= <gadget id="calculator">1*3</gadget> <output>3</output> 3 3*3= <gadget id="calculator">3*3</gadget> <output>9</output> 9 9*3= <gadget id="calculator">9*3</gadget> <output>27</output> 27 27*3= <gadget id="calculator">27*3</gadget> <output>81</output> 81 81*3= <gadget id="calculator">81*3</gadget> <output>243</output> 243 ANSWER:243 <result>D</result>

D

3,9,27,81,....

aqua_rat__TL6idH5UXf8VpPoS

A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics? Choose the correct choice from the following answers: A) 21 B) 27 C) 26 D) 80 E) 28

Given M + P + C = 80 * 3= <gadget id="calculator">80 * 3</gadget> <output>240</output> 240 --- (1) M + P= 90 * 2= <gadget id="calculator">90 * 2</gadget> <output>180</output> 180 --- (2) P + C= 70 * 2= <gadget id="calculator">70 * 2</gadget> <output>140</output> 140 --- (3) Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry. P= (2) + (3) - (1) = 180 + 140 - 240= <gadget id="calculator">180 + 140 - 240</gadget> <output>80</output> 80.Answer: 80 <result>D</result>

D

A student scored an average of 80 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?

aqua_rat__DJPTF6E4ygDORWXH

A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than six people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month? Choose the correct choice A) x/15 B) x/30 C) x/6 D) x/5 E) 5x/6

If 6 people share the rent, each person would pay x/6. If 5 people share the rent, each person will pay x/5. The extra amount each person pays is x/5 - x/6 = 6x/30 - 5x/30 = x/30 The answer is x/30. <result>B</result>

B

A group of college friends plan to rent a house together for x dollars per month, which is to be shared equally among them. If five, rather than six people rent the house together, how many more dollars, in terms of x, will each person have to pay for rent per month?

aqua_rat__cuk23V9e9Iq19gqt

If P represents the product of the first 13 positive integers, which of the following must be true? I. P is an even number II. P is a multiple of 6 III. P is a multiple of 24 Choose the correct choice from the following. A) I only B) II only C) III only D) None of the above E) All of the above

The correct answer is All of the above. <result>E</result>

E

If P represents the product of the first 13 positive integers, which of the following must be true? I. P is an even number II. P is a multiple of 6 III. P is a multiple of 24

aqua_rat__7p6KTrSWe07Dx9rw

The price of 5 kilograms of premium fertilizer is the same as the price of 8 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer? Options A) y/30 B) 5/6*y C) 6/5*y D) 5y E) 8y/3

Usingpfor premium andrfor regular, I got two equations from the question stem: 5p = 8r and p = r+y Substitute for p: 5(r+y) = 8r Distribute: 5r + 5y = 8r Subtract 5r from both sides: 5y = 3r Plug back into the first equation: 5p = 8(5y/3) Distribute: 5p = 40y/3 Divide both sides by 5: p = 8y/3 The answer is 8y/3. <result>E</result>

E

The price of 5 kilograms of premium fertilizer is the same as the price of 8 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?

aqua_rat__VnlKNRWwYNAy5mt6

s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Q are in s(99)? Choose the correct answer A) Q=350 B) Q=353 C) Q=354 D) Q=356 E) 357

Focus on the points where the number of digits Q in squares change: 1, 2, 3 - Single digit squares. First 2 digit number is 10. 4 , 5,...9 - Two digit squares. To get 9, the last number with two digit square, think that first 3 digit number is 100 which is 10^2. so 9^2 must be the last 2 digit square. 10, 11, 12, ... 31 - Three digit squares. To get 31, think of 1000 - the first 4 digit number. It is not a perfect square but 900 is 30^2. 32^2 = 2^10 = 1024, the first 4 digit square. 32 - 99 - Four digit squares. To get 99, think of 10,000 - the first 5 digit number which is 100^2. So number of digits in s(99) = 3*1 + 6*2 + 22*3 + 68*4 = 3 + 12 + 66 + 272= <gadget id="calculator">3 + 12 + 66 + 272</gadget> <output>353</output> 353.Q=353 <result>B</result>

B

s(n) is a n-digit number formed by attaching the first n perfect squares, in order, into one integer. For example, s(1) = 1, s(2) = 14, s(3) = 149, s(4) = 14916, s(5) = 1491625, etc. How many digits Q are in s(99)?

aqua_rat__2XIQAoGgy40emiag

If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is? Choose the correct choice from the following: A) 20:15:16 B) 20:15:68 C) 20:15:12 D) 20:15:11 E) 20:15:19

6A = 8B = 10 20:15:12 A:B:20:15:12 = 1/6:1/8:1/10 = 20:15:12 Answer: 20:15:12 <result>C</result>

C

If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?

aqua_rat__MVwVNB8td1iuv0bV

A pizzeria in Castroville creates its own special blend of shredded cheese at a cost of $696.05 per kilogram. The blend includes Mozzarella, at $504.35 per kilogram, and Romano cheese, at $887.75 per kilogram. If the employees have already shredded 19 kilograms of Mozzarella cheese, how many kilograms of Romano cheese will they need to shred now? Choose the correct choice from the following A) 19kg B) 13kg C) 10kg D) 23kg E) 15kg

504.35(19)+887.75x =696.05(19 + x) Solve the equation. 504.35(19) + 887.75x = 696.05(19 + x) 9,582.65 + 887.75x = 13,224.95 + 696.05x 9,582.65 + 191.7x = 13,224.95 191.7x = 3,642.3 x = 19 . 19kgnswer is 19kg. <result>A</result>

A

A pizzeria in Castroville creates its own special blend of shredded cheese at a cost of $696.05 per kilogram. The blend includes Mozzarella, at $504.35 per kilogram, and Romano cheese, at $887.75 per kilogram. If the employees have already shredded 19 kilograms of Mozzarella cheese, how many kilograms of Romano cheese will they need to shred now?

aqua_rat__OLglhJwSnAFNEcB6

A sum of money becomes triple itself in 16 years. In how many years will it become 5 times at the same rate? Choose the correct answer: A) 32 B) 15 C) 27 D) 30 E) 35

Let sum be Rs.100. After 16 years it become 300. With in 16 years it increased Rs.200 i.e. after 8 years it is doubled. So after 32 years interest become Rs.400. Total Rs.500 i.e. 5 times more than the sum. So 32 years is the answer. 32NSWER:32 <result>A</result>

A

A sum of money becomes triple itself in 16 years. In how many years will it become 5 times at the same rate?

aqua_rat__hJ4pSDUCen155DjC

How many positive integers less than 50 are multiples of 6 but NOT multiples of 8? Choose the correct choice: A) 4 B) 6 C) 8 D) 10 E) 12

The LCM of 6 and 8 is 24. If x &lt;50 and x is divisible by 6 not by 8 --&gt; x is NOT divisible by 24. From 1--&gt; 50, we have 2 numbers which is divisible by 24: 24, 48. From 1--&gt;50, we have (48-6)/6 +1= <gadget id="calculator">(48-6)/6 +1</gadget> <output>8</output> 8 numbers divisible by 6. Therefore, our answer is 8-2= <gadget id="calculator">8-2</gadget> <output>6</output> 6 numbers. 6 <result>B</result>

B

How many positive integers less than 50 are multiples of 6 but NOT multiples of 8?

aqua_rat__JVFKtHqyaZvtuFgF

Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 10 cm and 6 cm? Pick: A) 189 cm2 B) 150 cm2 C) 240 cm2 D) 177 cm2 E) 187 cm2

1/2 * 30(10 + 6) = 240 cm2 Answer: 240 cm2 <result>C</result>

C

Find the area of the quadrilateral of one of its diagonals is 30 cm and its off sets 10 cm and 6 cm?

aqua_rat__dc6xTVsnp5nmM7no

A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is? A. 31 B. 41 C. 51 D. 61 Choose the most appropriate option: A) 31 B) 41 C) 51 D) 61 E) 71

LCM = 30 =&gt; 30 + 1 = 3 31NSWER:31 <result>A</result>

A

A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left over. The least number of Coconuts in the heap is? A. 31 B. 41 C. 51 D. 61

aqua_rat__t3TuZvdxYoY69rys

Which of the following is the sum of all the even numbers between 1 and 93, inclusive? Select the correct option: A) 2550 B) 2450 C) 2600 D) 2447 E) 2652

This question can be solved withbunching. We're asked for the SUM of all of the EVEN integers from 1 to 99, so we really want the sum of 2, 4, 6, 8.....98. If you take the next smallest and next biggest numbers, you have... 8+92= <gadget id="calculator">8+92</gadget> <output>100</output> 100 This pattern will continue on, so we're going to have a bunch of 100s, BUT we have to be careful to make sure that we don't miss a number if it'sin the middleand doesn't get paired up. Since we know that the sum of each pair is 100, we can 'jump ahead' to find the last few pairs... 44+56= <gadget id="calculator">44+56</gadget> <output>100</output> 100 46+54= <gadget id="calculator">46+54</gadget> <output>100</output> 100 48+52= <gadget id="calculator">48+52</gadget> <output>100</output> 100 There IS a middle number: 50; this number does NOT get paired up. Since 48 is the 24th even integer, we know there are twenty-four 100s + one 50. 2400+50-3= 2447 Final Answer: 2447 <result>D</result>

D

Which of the following is the sum of all the even numbers between 1 and 93, inclusive?

aqua_rat__jg3BTOPMK5fdaHLH

A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour? Choose the correct choice from the following: A) 72 B) 84 C) 96 D) 108 E) 120

Each side of the cube has 6 x 6 = 36 cubelets. Only the interior cubelets are painted one colour. On each side, 4 x 4 = 16 cubelets are painted one colour. Since the cube has six sides, the number of cubes with one colour is 6*16= <gadget id="calculator"> 6*16</gadget> <output>96</output> 96 The answer is 96. <result>C</result>

C

A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of the cube. But before doing that, the cube is painted with green on one set of opposite faces, red on another set of opposite faces, and blue on the third set of opposite faces. How many cubelets are painted with exactly one colour?

aqua_rat__kMzu3uZCebBfLOsP

A man engaged a servant on the condition that he would pay him Rs.710 and a uniform after a year service. He served only for 8 months and got Rs.460 and a uniform. Find the price of the uniform? Options: A) Rs.40 B) Rs.30 C) Rs.25 D) Rs.20 E) Rs.45

8/12 = 2/3 * 710 = 473.33 460.00 --------------- 13.33 1/3 uniform 13.33 1 --------------- ? =&gt; Rs.40 Rs.40NSWER:Rs.40 <result>A</result>

A

A man engaged a servant on the condition that he would pay him Rs.710 and a uniform after a year service. He served only for 8 months and got Rs.460 and a uniform. Find the price of the uniform?

aqua_rat__6QxQ0UGXLrPphqH9

Tanya prepared 4 different letters to 3 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? Choose the correct choice from the following answers. A) 1/24 B) 1/8 C) 1/4 D) 1/3 E) 3/8

I hope you are familiar with basic probability fundas - Let's say you have just ONE letter and TWO envelopes ONE of which is correctly addressed and the other addressed incorrectly. What's the probability of putting the Letter in the correctly addressed envelope - To answer this question - we see IN HOW MANY WAYS can the letter be put into the envelope - you could put it (assuming you don't know which envelope is which) in either of the two - so in total you have TWO ways of shoving the letter in. However, there's only ONE way in which it can go into the correctly addressed envelope - so 1/2 is the prob of putting in correct envelope. This is easy. Now in our current problem - let's say we have just ONE letter but FOUR envelopes. Only one of these envelopes has the address corresponding to the letter. The remaining three envelopes are incorrectly addressed. So the probability that you will put the letter correctly is 1/4. Right? What happens if i ask you the reverse question? what is the prob for putting it in the incorrect envelope. Suddenly you have three envs that are incorrect so you can put the letter incorrectly with a prob of 3/4. Right? The whole problem can be broken down into Four Events that will fulfill the requirement of the question Event 1 - E1 We know that prob of putting ONE Letter correctly is 1/4. Now once ONE letter has been put CORRECTLY, what are you LEFT with? You are left with THREE ENVELOPES and the remaining THREE letters. Since the one letter has been put correctly (though technically we have just calculated the PROBABILITY that the first letter goes into the correct envelope) we have the remaining THREE Letters and THREE envelopes. Event 2 - E2 Let's take letter number 2 now - what is the probability that it LANDS in the INCORRECT envelope. Again by the same logic as above - there are 3 envelopes remaining out of which ONLY ONE has the correct address for LETTER number 2. The remaining 2 have INCORRECT address and LETTER NUMBER 2 could go in either of these 2 to meet our condition. Thus the probability of this event is 2/3 So till now what we have done is - we have calculated the prob of shoving Letter number 1 in correct env -- 1/4 we have calculated the prob of shoving Letter number 2 in INcorrect env --- 2/3 Event 3 - E3 Now let's take letter number 3 - again according to question we want to shove this in the WRONG envelope. There are 2 remaining envelopes and hence the prob of shoving this in the wrong env (or equally in the RIght env) is 1/2. Finally we come to event E4 - the Letter number 4. This has only one way of going in so its probability of being put into the WRONG envelope is 1. ok so we can see that our grand event is actually a combination of FOUR EVENTS happening - each with a probability of its own. So to calculate the total probability of the Grand Event itself we just multiply the individual probabilities since each event happens INDEPENDENTLY of each other Egrand = 1/4 * 2/3 * 1/2 * 1/1 = 1/12 However at this point - I must introduce one last element in this question -since there are FOUR Letters - what we saw above was JUST ONE SEQUENCE of events leading to the desired result. If we arbitrarily call the letters L1 thru L4, and let's say the above was an example in which we started by Picking up Letter L1 and worked thru the remaining letters, we could have equally well started out with letter L2 or L3 or L4. Thus since each of these events ARE MUTUALLY EXCLUSIVE, meaning THEY CAN NEVER HAPPEN ALL THE SAME TIME BUT ONLY ONE LETTER AT A TIME, to calculate the TOTAL PROBABILITY of we will add the individual probabilities 1/12 + 1/12 + 1/12 + 1/12 which works out to 1/4. 1/4 <result>C</result>

C

Tanya prepared 4 different letters to 3 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?

aqua_rat__qRFgXpHlRyIdwH3n

Set R has a mean of 11 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? Choose the correct choice from the following answers. A) {15, 13} B) {11, 14} C) {10, 12} D) {14, 19} E) {14, 11}

The lesser the variance( values closer to mean) ,lower the standard deviation. As discussed in question the mean is 11,the values (10,12) are closer than others. Hence Answer : {10, 12} <result>C</result>

C

Set R has a mean of 11 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most?

aqua_rat__mnyxKEG6rVoJq7wG

There are 9 orators A, B, C, D, E, F, G,H and I. In how many ways can the arrangements be made so that A always comes before B and B always comes before C. Options. A) 9! / 3! B) 8! / 6! C) 5! x 3! D) 8! / (5! x 3!) E) 8! / (5! x 4!)

Select any three places for A, B and C. They need no arrangement amongst themselves as A would always come before B and B would always come before C. The remaining 6 people have to be arranged in 6 places. Thus, 9C3 x 6! = 9! / 3! 9! / 3!NSWER:9! / 3! <result>A</result>

A

There are 9 orators A, B, C, D, E, F, G,H and I. In how many ways can the arrangements be made so that A always comes before B and B always comes before C.

aqua_rat__bFfOM4CfqFPrhRq3

A circular rim A having a diameter of 24 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 30 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation. Choose the correct choice from the following answers: A) 5x/4 B) 4x/3 C) 6x/5 D) 8x/7 E) 9x/8

t = S1/V1 = S2/V2 or, 24/x = 30/y or, y = 30x/24 = 5x/4 (5x/4nswer 5x/4) <result>A</result>

A

A circular rim A having a diameter of 24 inches is rotating at the rate of x inches/min. Another circular rim B with a diameter of 30 inches is rotating at the rate of y inches/min. What is the value of y in terms of x, if both the rims reach their starting positions at the same time after every rotation.

aqua_rat__pzrREbVAuov9c27v

What is the value of 1×1!+2×2!+3!×3!+............n×n!;where n! means n factorial or n(n−1)(n−2)...1 Pick one: A) n(n−1)(n−1)! B) n(n−1)(n−1)! C) n(n−1)(n−1)! D) (n+1)!−1! E) None of these

Explanation : 1×1!=(2−1)×1!=2×1!−1×1!=2!−1!2×2!=(3−1)×2!=3×2!−2!=3!−2!3×3!=(4−1)×3!=4×3!−3!=4!−3!......n×n!=(n+1−1)×n!=(n+1)(n!)−n!=(n+1)!−n!Summing up all these terms, we get (n+1)! - 1! Answer : (n+1)!−1! <result>D</result>

D

What is the value of 1×1!+2×2!+3!×3!+............n×n!;where n! means n factorial or n(n−1)(n−2)...1

aqua_rat__osI4kOmkM4FhtGol

Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms? Choose the correct answer. A) 30 km per hour B) 32 km per hour C) 49 km per hour D) 54 km per hour E) 65 km per hour

Given that the diesel consumption is at the rate 1400×[1000x+x]1400×[1000x+x] Cost of diesel = Rs 35 per litre Payment to the driver = Rs 125 per hour. Also given that the SUV is driven at the speed of xx km per hour. Total cost (c)(c) =1400×[1000x+x]×800×35+125×800x=1400×[1000x+x]×800×35+125×800x =70000x+70x+100000x=70000x+70x+100000x Now differentiating both sides in the above equation with respect to xx. dcdx=−170,000x2+70=0dcdx=−170,000x2+70=0 ⇒ x=49 km per hour. 49 km per hour <result>C</result>

C

Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx km per hour. If the cost of diesel is Rs 35 per litre and the driver is paid at the rate of Rs 125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms?

aqua_rat__R2ebTFXX6eBzHK5D

The ratio of two numbers is 3:4 and their sum is 21. The greater of the two numbers is? Choose the correct choice A) 12 B) 14 C) 16 D) 17 E) 19

3:4 Total parts = 7 = 7 parts --&gt; 21 (7 × 3 = 21) = 1 part ----&gt;3 (1 × 3 = 4) = The greater of the two number is = 4 = 4 parts ----&gt; 12 (4 × 3 = 12) 12 <result>A</result>

A

The ratio of two numbers is 3:4 and their sum is 21. The greater of the two numbers is?

aqua_rat__zxVHkYdAr418wpyH

A plane flies 880 km with the wind and 720 km against the wind in the same length of time. If the speed of the wind is 20 km/h, what is the speed of the plane in still air? Pick: A) 140 km/h B) 160 km/h C) 180 km/h D) 200 km/h E) 220 km/h

The speed of the plane in still air = x km/h The speed of the wind is 20 km/h Speed with the wind = (x + 20) km/h Speed against the wind = (x – 20) km/h Time = Distance/ Speed 880 / (x+20) = 720 / (x-20) 880(x-20) = 720(x+20) 88x - 1760 = 72x + 1440 16x = 3200 x = 200 Therefore, the speed of the plane in still air is 200 km/h. The answer is 200 km/h. <result>D</result>

D

A plane flies 880 km with the wind and 720 km against the wind in the same length of time. If the speed of the wind is 20 km/h, what is the speed of the plane in still air?

aqua_rat__zX81iz8X35elLBbj

Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 24 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)? Select the correct option A) 12 km/hr B) 16 km/hr C) 20 km/hr D) 24 km/hr E) 28 km/hr

Let the speed of the slower train be x m/s Then, the speed of the faster train is 2x m/s The relative speed is 3x m/s (100 + 100)/24 = 3x x = 25/9 m/s So, the speed of the faster train is 50/9 = 50/9 * 18/5= <gadget id="calculator">50/9 * 18/5</gadget> <output>20</output> 20 km/hr The answer is 20 km/hr. <result>C</result>

C

Two trains, each 100 meters long, moving in opposite directions, completely pass each other in 24 seconds. If one train is moving twice as fast the other, then what is the speed of the faster train (in km/hr)?

aqua_rat__GltfjsqtsjSioMSA

We can rent a cabin for x dollars per day for the first 5 days and then y dollars for each additional day. How much will it cost to rent a cabin for z days, where z>5? Pick A) 5x + zy B) 5y+(z-5)x C) xz + 5y D) 5x - z + y E) 5x+(z-5)y

The first 5 days cost 5x. The next (z-5) days cost (z-5)y. The total cost is 5x+(z-5)y. The answer is 5x+(z-5)y. <result>E</result>

E

We can rent a cabin for x dollars per day for the first 5 days and then y dollars for each additional day. How much will it cost to rent a cabin for z days, where z>5?

aqua_rat__of9Vzg1bM8JZh9Tw

By selling a book for 290, 20% profit was earned. What is the cost price of the book? Choose the most appropriate option: A) A)215 B) B)241 C) C)230 D) D)235 E) E)240

SP = 120% of CP; :. CP = 290 × 100/120 = 241 Option '241' <result>B</result>

B

By selling a book for 290, 20% profit was earned. What is the cost price of the book?

aqua_rat__Y2t3pSduCCSrdsMg

One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs. 120 and a shirt.Then find the price of the shirt. Choose the correct answer: A) 126 B) 217 C) 127 D) 120 E) 182

12 months == Rs 200 + shirt --(1) 9 months == Rs 120 + shirt --(2) After subtracting equation (2) from (1) we get,(shirt is cancelled) 3 months = Rs 80 12 months = (80 × 12)/3= 320 Hence from equation (1) we get 320 = 200 + shirt Therefore shirt = 120 Rs/- Answer: 120 <result>D</result>

D

One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and receives Rs. 120 and a shirt.Then find the price of the shirt.

aqua_rat__Xym0wHIMbArC3k2W

Three friends Ram, Rahul and Raj divide $1000 amongs them in such a way that if $1, $2 and $8 are removed from the sums that Ram, Rahul and Raj received respectively, then the share of the sums that they got will be in the ratio of 6 : 7 : 10. How much did Raj receive? Choose the correct choice: A) $434 B) $458 C) $438 D) $448 E) $478

Explanatory Answer Let the sums of money received by A, B and C be x, y and z respectively. Then x - 1 : y - 2 : z -8 is 6a : 7a : 10a When $1, $2 and $8 are removed, we are removing a total of $11 from $1000. Therefore, 6a + 7a + 10a = 1000 - 11= <gadget id="calculator">1000 - 11</gadget> <output>989</output> 989 i.e., 23a= 989 or a = 43 We know that z - 8 = 10a = 10 * 43= <gadget id="calculator">10 * 43</gadget> <output>430</output> 430 Therefore, z= 430 + 8= <gadget id="calculator">430 + 8</gadget> <output>438</output> $438 The correct choice is (c) <result>C</result>

C

Three friends Ram, Rahul and Raj divide $1000 amongs them in such a way that if $1, $2 and $8 are removed from the sums that Ram, Rahul and Raj received respectively, then the share of the sums that they got will be in the ratio of 6 : 7 : 10. How much did Raj receive?

aqua_rat__we1EOoL3vnHT1xdC

What is the smallest possible common multiple of three integers, all larger than 22? Choose the correct choice from the following answers: A) 27. B) 54. C) 846. D) 19,656. E) 23

The Least common positive multiple would be for the immediate least number(s) after 22 i.e 22. Since nowhere is it stated that the three integers must be different, the integers could be 22,22 and 22... leading to least possible positive common multiple to be 22. Answer 23. <result>E</result>

E

What is the smallest possible common multiple of three integers, all larger than 22?

aqua_rat__vSj9exGAZ1imf5dE

The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years R in which the population would be doubled assuming there is no emigration or immigration is Choose the correct choice from the following choices: A) 20 B) R=25 C) R=30 D) R=35 E) 40

Suppose the population of the country in current year is 1000. So annual increase is 1000 + 39.4 - 19.4= <gadget id="calculator"> 1000 + 39.4 - 19.4</gadget> <output>1_020</output> 1020 Hence every year there is an increase of 2%. 2000= 1000(1+(2/100))^n n=35 Answer is R=35. <result>D</result>

D

The annual birth and death rate in a country per 1000 are 39.4 and 19.4 respectively . the number of years R in which the population would be doubled assuming there is no emigration or immigration is

aqua_rat__D3hXOjuQjoyPZa5H

If Jan 1, 2006 was a Friday, What was the day of the week Jan 1, 2010? Choose the correct choice from the following options. A) Friday B) Thursday C) Tuesday D) Saturday E) Wednesday

Explanation : Given that Jan 1 2006 was a Friday Number of odd days in the period 2006-2009 = 3 normal years + 1 leap year = 3 x 1 + 1 x 2 = 5 (note that we have taken the complete year 2006 because the period in 2006 is from 01-Jan-2006 to 31-Dec-2006, which is the whole year 2006. Then the complete years 2007, 2008 and 2009 are also involved) Hence Jan 1 2010 = (Friday + 5 odd days) = Wednesday.. Answer : Option Wednesday <result>E</result>

E

If Jan 1, 2006 was a Friday, What was the day of the week Jan 1, 2010?

aqua_rat__Mfs4MAYrFPjXO02l

A 6-liter solution is 35% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol? Choose the correct option: A) 1.5 B) 1.8 C) 2.1 D) 2.4 E) 2.7

Let x be the amount of pure alcohol required. 0.35(6) + x = 0.5(x+6) 0.5x = 3 - 2.1 x = 1.8 liters The answer is 1.8. <result>B</result>

B

A 6-liter solution is 35% alcohol. How many liters of pure alcohol must be added to produce a solution that is 50% alcohol?

aqua_rat__4OY0bTVhgSSe4aFC

At what rate of interest (compounded yearly)will Rs.10,000 amount to Rs.12100 in 2 years? Choose the correct choice. A) 9% B) 11% C) 8% D) 10% E) 20%

If rate=r, then 10000[1+(r/100)]^2 =12100 ,(100+r)^2 /100^2 =121 r^2 +200r -2100=0 (r-10)(r+210)=0 r=10 ANSWER:10% <result>D</result>

D

At what rate of interest (compounded yearly)will Rs.10,000 amount to Rs.12100 in 2 years?

aqua_rat__FxjfVVKnQrEsh6Wh

A thief is spotted by a policeman from a distance of 160 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken? Choose one: A) 350m B) 240m C) 440m D) 640m E) None of them

Relative speed of the policeman = (10-8) km/hr =2 km/hr. Time taken by police man to cover (160m/1000) x 1/2 hr = 2/25hr. In 2/25 hr/s, the thief covers a distance of 8 x 2/25 km = 16/25 km = 640 m Answer is 640m. <result>D</result>

D

A thief is spotted by a policeman from a distance of 160 meters. When the policeman starts the chase, the thief also starts running. If the speed of the thief be 8km/hr and that of the policeman 10 km/hr, how far the thief will have run before he is overtaken?

aqua_rat__i7uA5Kp5hP2PYTXG

A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it? Choose the most appropriate option. A) 110 B) 120 C) 128 D) 134 E) 154

First Purchased = 250 Wes= 128 128 <result>C</result>

C

A watch passes through three hands and each gains 25%. If the 3rd sells it for Rs250, what did the 1st pay for it?

aqua_rat__dzABbA7oQFalHpwA

A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water? Choose the correct choice from the following options: A) 22 B) 77 C) 30 D) 99 E) 12

US = 25 DS = 35 M = (35 + 25)/2= <gadget id="calculator">(35 + 25)/2</gadget> <output>30</output> 30 Answer: 30 <result>C</result>

C

A man can row upstream at 25 kmph and downstream at 35 kmph, and then find the speed of the man in still water?

aqua_rat__9QtrH3P75oajihvC

((1^5m)/(5^5m))((1^18)/(4^18)) = 1/(2(10)^35) What is m? Choose the correct choice: A) 7 B) 18 C) 34 D) 35 E) 36

((1^5m)/(5^5m))((1^18)/(4^18)) = 1/(2(10)^35) ((1/5)^5m ) * ((1/2)^36) = 1/ (2 * (2*5)^35)) 2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^5m= (1/5)^35 ((1/5)^5m ) * ((1/2)^36) = 1/[(2^36)*(5^35)] So, m=7 7nswer 7 <result>A</result>

A

((1^5m)/(5^5m))((1^18)/(4^18)) = 1/(2(10)^35) What is m?

aqua_rat__vr7eT21yzsMCWf5C

Mary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income? Options A) 124% B) 120% C) 96% D) 80% E) 84%

Juan's income = 100 (assume); Tim's income = 60 (40 percent less than Juan's income); Mary's income = 84 (40 percent more than Tim's income). Thus, Mary's income (84) is 84% of Juan's income (100). Answer: 84%. <result>E</result>

E

Mary's income is 40 percent more than Tim's income, and Tim's income is 40 percent less than Juan's income. What percent of Juan's income is Mary's income?

aqua_rat__Mk27MXzOZvFEkrZz

What strength of 20 ml alcohol should be added to 10ml of 50% alcohol to get an average strength of 20% alcohol. Answers A) 0.5 % B) 5 % C) 50 % D) 5.5 % E) 0.05 %

20*x + 10*0.5 = (20 + 10)*0.2 --&gt; x = 0.05 = 5%. Answer: 5 %. <result>B</result>

B

What strength of 20 ml alcohol should be added to 10ml of 50% alcohol to get an average strength of 20% alcohol.

aqua_rat__QyJsLlQYQfvqLm0J

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was: Choose the correct choice from the following options: A) 2800 B) 2700 C) 2900 D) 2200 E) 2300

B Number of valid votes = 80% of 7500 = 6000. Valid votes polled by other candidate = 45% of 6000 = (45/100 x 6000) = 2700. <result>B</result>

B

In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

aqua_rat__qTkrjfnl0yYhPXBE

How much is 80% of 45 is greater than 4/5 of 25? Choose the correct choice from the following options: A) 15 B) 57 C) 16 D) 16 E) 73

(80/100) * 45 – (4/5) * 25 36 - 20= <gadget id="calculator">36 - 20</gadget> <output>16</output> 16 Answer: 16 <result>C</result>

C

How much is 80% of 45 is greater than 4/5 of 25?

aqua_rat__luS6LoX7IjnaQasr

A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.695 in all. Find the share of B? Choose the correct choice: A) 130 B) 120 C) 218 D) 144 E) 145

A+B+C = 695 A = 3B 3B+B+B-25 = 695 5B = 720 B = 144 Answer: 144 <result>D</result>

D

A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.695 in all. Find the share of B?

aqua_rat__eG93lKQ9NPa360jU

A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 630 m? Choices: A) 120 sec B) 99 sec C) 89 sec D) 87 sec E) 85 sec

Explanation: v = 240/24 (where v is the speed of the train) = 10 m/s t = (240+630)/10= <gadget id="calculator">(240+630)/10</gadget> <output>87</output> 87 seconds Answer: Option 87 sec <result>D</result>

D

A train having a length of 240 m passes a post in 24 seconds. How long will it take to pass a platform having a length of 630 m?

aqua_rat__kK8AVZoYxR1mwjGW

In the coordinate plane, a circle centered on point (-3, 4) passes through point (1, 1). What is the area of the circle? Choose the correct choice from the following choices. A) 9π B) 18π C) 25π D) 37π E) 41π

r^2=(-3-1)^2+(4-1)^2=16+9= <gadget id="calculator">16+9</gadget> <output>25</output> 25 Area of circle=πr^2=25π Answer : 25π <result>C</result>

C

In the coordinate plane, a circle centered on point (-3, 4) passes through point (1, 1). What is the area of the circle?

aqua_rat__Tj0bgIEghiDffIZD

A coin is tossed two times. What is the probability that there is at the least one tail? Choose the correct choice from the following answers A) 3/4 B) 1/3 C) 3/7 D) 3/5 E) 1/31

Let P(T) be the probability of getting least one tail when the coin is tossed two times. = There is not even a single tail. i.e. all the outcomes are heads. = 1/4 ; P(T) = 1 - 1/4 = 3/4 3/4nswer: 3/4 <result>A</result>

A

A coin is tossed two times. What is the probability that there is at the least one tail?

aqua_rat__a4Uw1vMnlLF1KbLz

Two-third of a positive number and 144/216 of its reciprocal are equal. The number is: Select. A) 5/12 B) 12/5 C) 25/144 D) 144/25 E) 1

Let the number be x. Then, 2/3 x = 144/216 * 1/x x2 = 144/216 * 3/2 = 144/144= <gadget id="calculator">144/144</gadget> <output>1</output> 1 ANSW1R:1 <result>E</result>

E

Two-third of a positive number and 144/216 of its reciprocal are equal. The number is:

aqua_rat__gMVCX08w5j3LVrI7

A son and father goes for boating in river upstream . After rowing for 1 mile son notices the hat of his father falling in the river. After 5 min he tells his father that his hat has fallen. So they turn round and are able to pick the hat at the point from where they began boating after 5min. Find the speed of river in miles/hours ? Select: A) 7 mile/hr B) 6 mile/hr C) 8 mile/hr D) 1 mile/hr E) 2 mile/hr

Explanation: Let the speed of river and boat be 'r' m/min and 'b' m/min. so relative speed in upstream (b-r)m/min and in downstream (b+r)m/min. Now in upstream distnce covered in 5 min is 5(b-r)miles so total distnce covered =&gt; 1 + 5(b-r)miles in upstream In downstream distance covered in 5min is 5(b+r)miles Now 1 + 5(b-r) = 5(b+r) 1+5b-5r = 5b+5r 1 = 10r r = 1/10 mile/min =&gt; 6 mile/hr. Answer: 6 mile/hr <result>B</result>

B

A son and father goes for boating in river upstream . After rowing for 1 mile son notices the hat of his father falling in the river. After 5 min he tells his father that his hat has fallen. So they turn round and are able to pick the hat at the point from where they began boating after 5min. Find the speed of river in miles/hours ?

aqua_rat__HPt1q8K9qJNizKvn

The balance of a trader weighs 20% less than it should. Still the trader marks up his goods to get an overall profit of 30%. What is the mark up on the cost price? Choose the correct choice from the following options: A) 4% B) 8% C) 25% D) 16.66% E) 9%

The most natural way to deal with 'weights' questions is by assuming values. Say the trader's balance shows 100 gms. It is actually 80 gms because it weighs 20% less. Say, the cost price is $80 ($1/gm). Since he gets a profit of 30%, the selling price must be 80+(30/100)*80= <gadget id="calculator">80+(30/100)*80</gadget> <output>104</output> $104 Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $104, the mark up is simply 4%. 4%ns : 4% <result>A</result>

A

The balance of a trader weighs 20% less than it should. Still the trader marks up his goods to get an overall profit of 30%. What is the mark up on the cost price?

aqua_rat__1qkJ7X5Tm7YXCfOE

A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 310 m long? Answers: A) 34 Seconds B) 22 Seconds C) 41 Seconds D) 24 Seconds E) 27 Seconds

27 Seconds Distance travelled = 140 + 310= <gadget id="calculator">140 + 310</gadget> <output>450</output> 450m Speed= 60 * 5/8 = 50/3m Time = 450 * 3/50= <gadget id="calculator">450 * 3/50</gadget> <output>27</output> 27 Seconds ANSW27 SecondsR 27 Seconds <result>E</result>

E

A bullet train 140 m long is running at 60 kmph. In how much time will it pass a platform 310 m long?

aqua_rat__m8NXaViQUfajoXuU

If a and b are integers and (2^a)(3^b) is a factor of 180^40, what is the largest possible value of ab? Choose the correct choice from the following answers A) 2a B) 5a C) 20a D) 40a E) 80a

(2^a)(3^b) is a factor of 180^40 We need to find the largest possible value of ab. We know that 180 = 2^2*5^1*3^2 Therefore 180^40 will have 2 powers of 3 in it. Hence in (2^a)(3^b), b has to 2 Therefore value of ab = 2a Correct Option: 2a <result>A</result>

A

If a and b are integers and (2^a)(3^b) is a factor of 180^40, what is the largest possible value of ab?

aqua_rat__cEVPslZvgxrgAOBU

Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight. Answers. A) 22 B) 10 C) 88 D) 26 E) 18

M + D + I = 74 - - - (1) (D + I) - M = 46 - - - (2) I = 410410 D ⇒⇒ 5I = 2D ⇒⇒ I = 2D/5 - - - (3) Adding (1) and (2) we get 2D + 2I = 120 Substituting the value of I in the above equation, 2D+2(2D5)=1202D+2(2D5)=120 ⇒⇒ 14D = 600 ⇒⇒ D = 300/7 = 42.8 Ans:10 <result>B</result>

B

Weight of M, D and I is 74. Sum of D and I is 46 greater than M. I is 60% less than D. What is D's weight.

aqua_rat__2ymoHGVKe2WcJLMA

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is: Choose the correct option: A) 10 km/hr B) 50 km/hr C) 14 km/hr D) 17 km/hr E) 77 km/hr

Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==&gt; x = 50 km/hr. Answer: 50 km/hr <result>B</result>

B

A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is:

aqua_rat__vbySDEUyt2hAiTlG

A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? Choose the correct choice: A) 177 B) 166 C) 350 D) 198 E) 161

Speed = [300 / 18] m/sec = 50/3 m/sec. Let the length of the platform be x meters. Then, x + 300 / 39 = 50/3 3(x + 300) = 1950 è x = 350m. Answer: 350 <result>C</result>

C

A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?

aqua_rat__0c9jJDwqH2fnvkyT

One fourth of one third of two fifth of a number is 15. What will be the 40% of that number is? Choices: A) 120 B) 130 C) 150 D) 180 E) 250

(1/4) * (1/3) * (2/5) * x = 15 then x = 15 * 30= <gadget id="calculator">15 * 30</gadget> <output>450</output> 450 40% of 450= 180 ANSWER 180 <result>D</result>

D

One fourth of one third of two fifth of a number is 15. What will be the 40% of that number is?

aqua_rat__cGdooFjehpAuA5Dp

In a restaurant, the profit is 110% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit? Choose the correct answer: A) 30% B) 47% C) 90% D) 100% E) None of these

Explanation : Let C.P.= Rs. 100. Then, Profit = Rs. 110, S.P. = Rs. 210. New C.P. = 112% of Rs. 100 = Rs. 112 New S.P. = Rs. 210. Profit = Rs. (210 - 112) = Rs. 98. Required percentage = (98 /210 *100) % = 47 % appox Answer : 47% <result>B</result>

B

In a restaurant, the profit is 110% of the cost. If the cost increases by 12% but the selling price remains constant, approximately what percentage of the selling price is the profit?

aqua_rat__snvD4bCzTnEKO4Ng

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ? Choose the most appropriate option: A) -119 B) -159 C) -110 D) -180 E) -105

Explanation : Let, the quadratic equation be ax2 + bx + c. So, f(x) = ax2 + bx + c At x = 0, the value of function is 1. x = 0, f(x) = 1 ax2 + bx + c = a * 0 + b * 0 + c = c c = 1. At x = 1, f(x) = 3 x = 1, f(x) = 3 a *1 + b * 1 + c = 3 Since c = 1, a + b = 2. Also, we know that f(x) is maximum when x = 1. If f(x) is maximum, (dx/dt)(f(x)) = 0 Differentiating f(x), we have d/dt (ax2 + bx + c) = 2ax + b At x = 1, 2ax + b = 0. 2a + b = 0. b = -2a. Substituting we have a + b = 2, or a + -2a = 2. a = -2. So, b = 4. So the equation is -2x2 + 4x + 1. At x = 10, the value is -2 * 100 + 4 * 10 + 1 i.e -159. Answer : -159 <result>B</result>

B

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f(x) at x = 10 ?

aqua_rat__xsjvIYNA0p9NmSvW

A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ? Choose the correct choice from the following: A) 4 months B) 5 months C) 6 months D) 8 months E) 7 months

Suppose B joined for x months . Then, ( 85000 * 12 )/(42500 * x) = 3. or x = (85000 * 12) / (42500 * 3)= <gadget id="calculator">(85000 * 12) / (42500 * 3)</gadget> <output>8</output> 8. So, B joined for 8 months.Answer: 8 months <result>D</result>

D

A began a business with Rs. 85,000. He was joined afterwards by B with Ks. 42,500. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1 ?

aqua_rat__XBADFKMEq5IfunwR

Potato chips are on sale, buy 2 get 1 free. There are only 9 bags of chips left (4 plain and 5 bbq). A shopper randomly grabs 3 bags. What is the probability the shopper will grab exactly 3 bags of bbq chips? Choose the correct choice from the following: A) 2/3 B) 1/3 C) 1/5 D) 5/42 E) 7/42

Combination Probability Formula: nCr = n!/[r!(n-r)!] Total possible, select 3 bags from 9 bags = 9C3 = 9!/[3!(9 - 3)!] = 84. To have 3 bbq there must be 0 plain, select 0 plain from 4 = 4C0 = 1. And, select 3 bbq from 5 = 5C3 = 10. 3 bbq and 0 plain = (1)(10) = 10 Probability = (number outcomes favorable)/(total number outcomes) = 10/84 = 5/42 Answer: 5/42 <result>D</result>

D

Potato chips are on sale, buy 2 get 1 free. There are only 9 bags of chips left (4 plain and 5 bbq). A shopper randomly grabs 3 bags. What is the probability the shopper will grab exactly 3 bags of bbq chips?

aqua_rat__NzZTrbjwrfLkJj8a

A train 180 m long passed a pole in 3 sec. How long will it take to pass a platform 330 m long? Choices. A) 5 B) 6 C) 7 D) 8 E) 9

Speed = 180/3= <gadget id="calculator">180/3</gadget> <output>60</output> 60 m/sec. Required time= (180 + 300)/60= <gadget id="calculator">(180 + 300)/60</gadget> <output>8</output> 8 sec. Answer:8 <result>D</result>

D

A train 180 m long passed a pole in 3 sec. How long will it take to pass a platform 330 m long?

aqua_rat__7N4tVdhTAbIXOdZY

The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 32∘, the temperature of Friday was : Choose the correct choice from the following answers: A) 40∘ B) 39∘ C) 38∘ D) 30∘ E) None of these

Explanation: M+T+W+Th=(4×38)=152 Monday temperature is 32. So T+W+Th=(152-32)= <gadget id="calculator">(152-32)</gadget> <output>120</output> 120 T+W+Th+F=(4×40)=160 F = (160-120)= <gadget id="calculator">(160-120)</gadget> <output>40</output> 40∘ Correct Option: 40∘ <result>A</result>

A

The average temperature of Monday, Tuesday, Wednesday and Thursday was 38∘ and that of Tuesday, Wednesday, Thursday and Friday was 40∘. If the temperature on Monday was 32∘, the temperature of Friday was :

aqua_rat__B67d3gtHyFBVJDmZ

The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is? Answers: A) 0.5909 B) 0.5904 C) 0.5902 D) 0.5907 E) 0.5901

P(winning prize atleast on one ticket) = 1 - P("Losing on all tickets") = 1 - (0.8)4 = (1 + (0.8)2)(1 - (0.8)2) = (1.64)(0.36) = 0.5904 Answer:0.5904 <result>B</result>

B

The probability of a lottery ticket being a prized ticket is 0.2. When 4 tickets are purchased, the probability of winning a prize on atleast one ticket is?

aqua_rat__pGGgvftwK0T0XQVe

18 beavers, working together in a constant pace, can build a dam in 12 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam? Choose one. A) 2. B) 4. C) 5. D) 6 E) 18.

Total Work = 18*12= <gadget id="calculator">18*12</gadget> <output>216</output> 216 Beaver hours 12 Beaver * x=216Beaver hours x=216 / 12= <gadget id="calculator">216 / 12</gadget> <output>18</output> 18 ANSW18.R:18. <result>E</result>

E

18 beavers, working together in a constant pace, can build a dam in 12 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam?

aqua_rat__hZE1WYKCGLXlLyDR

The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is? Choose the correct answer: A) 299 B) 266 C) 299 D) 750 E) 261

Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec. Let the length of the train and that of the platform be x meters. Then, 2x/60 = 25 è x = 25 * 60 / 2= <gadget id="calculator">25 * 60 / 2</gadget> <output>750</output> 750 Answer: 750 <result>D</result>

D

The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?

aqua_rat__qMe3k1z3WBEWVW3a

A train running at the speed of 60 km/hr crosses a pole in 36 seconds. What is the length of the train? Choose the correct option: A) 186 m B) 176 m C) 100 m D) 600 m E) 765 m

Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 36)= <gadget id="calculator">(50/3 * 36)</gadget> <output>600</output> 600 m. Answer: 600 m <result>D</result>

D

A train running at the speed of 60 km/hr crosses a pole in 36 seconds. What is the length of the train?

aqua_rat__WWXi2Jpxr8SltLtL

What is the measure of the angle Y made by the diagonals of the any adjacent sides of a cube. Choose the correct choice from the following A) 30 B) 45 C) 60 D) 75 E) 90

C.. 60 degrees All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.60 <result>C</result>

C

What is the measure of the angle Y made by the diagonals of the any adjacent sides of a cube.