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NLP Centre, Faculty of Informatics, Masaryk University 14

aqua_rat__4GGcuR2RpW5Dbrnz

Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible? Choose one: A) 10 B) 21 C) 210 D) 420 E) 1,260

First Select 5 from 7 contestants and then select top 3 from those 5 = 72105*52103 = 42 * 5= <gadget id="calculator">42 * 5</gadget> <output>210</output> 210 ANS:210 <result>C</result>

C

Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?

aqua_rat__1JugrjDmqD7dw7Ly

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 40% marks is Choose the correct choice from the following options. A) 5 B) 4 C) 3 D) 2 E) 1

Here we can assume that one subject is of 100 marks so total there are 5 subjects =&gt; 100*5= <gadget id="calculator">100*5</gadget> <output>500</output> 500. Now according to the question he secured 60 % of those which is 60%of 500= 300 marks in total. The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio. Total ratio = 40 For 6 : (300/40)*6= <gadget id="calculator">(300/40)*6</gadget> <output>45</output> 45 Similarly , we will get for others as 52.5 , 60 , 62.5 , 75. Hence , there are 4 subject where he secured more that 40 %. The answer is 5. 5 <result>A</result>

A

A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 40% marks is

aqua_rat__7EK2wdsnlrBTXf80

If 7^w is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of w? Choose one: A) 12 B) 13 C) 14 D) 15 E) 16

So the question just means that we have to find all the multiples w of 7 between 1 to 100 So there are 14 multiples of 7 ( 7 - 98) But 49 and 98 contain two 7's as factors so we have to add 14 + 2= <gadget id="calculator"> 14 + 2</gadget> <output>16</output> 16 16 <result>E</result>

E

If 7^w is a factor of the product of the integers from 1 to 100, inclusive, what is the largest value of w?

aqua_rat__GxSmGtzke1VDEoaE

24 oz of juice P and 25 oz of juice V are mixed to make smothies A and Y . The ratio of p to V in smothie A is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie A? Choose the correct choice from the following options: A) 5 B) 10 C) 15 D) 20 E) 25

The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5. p1 + p2 = 24 v1 + v2 = 25 p1 = 4v1 p2 = v2/5 4v1 + v2/5 = 24 v1 + v2 = 25 4v2 - v2/5 = 76 19v2/5 = 76 =&gt; v2 = 20 =&gt; v1 = 5 =&gt; p1 = 20 Answer - 20 <result>D</result>

D

24 oz of juice P and 25 oz of juice V are mixed to make smothies A and Y . The ratio of p to V in smothie A is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie A?

aqua_rat__DseT6YKGBNw5xOqx

Lucy bought a 1-year,10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually. What was the total amount of interest paid on this certificate at maturity ? Select: A) 10464 B) 864 C) 816 D) 800 E) 480

Solution: It says, 8 percent per annum per compounded semi annually. Therefore r = 8/2= <gadget id="calculator">8/2</gadget> <output>4</output> 4% . So, P= 10000 r = 4 n = 2 Net Amount A = 10816, I = 800. ANSWER:800 <result>D</result>

D

Lucy bought a 1-year,10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually. What was the total amount of interest paid on this certificate at maturity ?

aqua_rat__32aRei5vrmC1biHo

A shop owner sells 30mtr of cloth and gains SP of 10 mtrs. Find the gain %? Choices: A) 30% B) 40% C) 50% D) 60% E) 70%

Here, selling price of 10 m cloth is obtained as profit. Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth) Selling price of 20 m cloth = Selling Price of 30 m of cloth Let cost of each metre be Rs. 100. Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000 Profit% = 10 × 100 = 50% 20 Profit of 50% was made by the merchant. 50% <result>C</result>

C

A shop owner sells 30mtr of cloth and gains SP of 10 mtrs. Find the gain %?

aqua_rat__zzxXe8S7nQGazxXk

For some integer x, x^2 - 5 is divisible by all of the following EXCEPT Choose the correct choice from the following. A) 41 B) 38 C) 29 D) 31 E) 30

Hint: x^2-5 (x is an integer) is never multiple of 3 (try to prove this), hence 30 is out. Answer: 30 <result>E</result>

E

For some integer x, x^2 - 5 is divisible by all of the following EXCEPT

aqua_rat__PrBwPSGYhZxQwhmy

The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue W, in dollars, from the sale of cars priced at $ 15,000? Choose the correct choice from the following options. A) 50,000 B) 750,000 C) 850,000 D) 7,500,000 E) W=750,000,000

number of cars sold = x=800000-50y y=15000 x=800000-750000= <gadget id="calculator">800000-750000</gadget> <output>50_000</output> 50000 revenue from 50000 cars=15000*50000= <gadget id="calculator">15000*50000</gadget> <output>750_000_000</output> 750000000 W=750,000,000 <result>E</result>

E

The number x of cars sold each week varies with the price y in dollars according to the equation x = 800,000 – 50y. What would be the total weekly revenue W, in dollars, from the sale of cars priced at $ 15,000?

aqua_rat__clFyOovsb0ag667r

In an election between two candidates, 75% of the voters cast thierthier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election. Choose the correct choice from the following answers: A) 1600 B) 16000 C) 16800 D) 1680 E) 16870

Let the number of votes enrolled be x. Then , Number of votes cast =75% of x. Valid votes = 98% of (75% of x). 75% of (98% of (75%of x)) =9261. [(75/100)*(98/100)*(75/100)*x] =9261. X = [(9261*100*100*100)/(75*98*75)= <gadget id="calculator">(9261*100*100*100)/(75*98*75)</gadget> <output>16_800</output> 16800. ANSWER 16800 16800 <result>C</result>

C

In an election between two candidates, 75% of the voters cast thierthier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.

aqua_rat__7U2NERhUY1FfGcbM

KODAK bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year? Choices: A) 1:5 B) 625:3125 C) 100:105 D) 100^4:105^4 E) 725:3225

Hi Bunuel, Here is my approach: is this correct? KODAK bank offers an interest of 5% per annum compounded annually on all its deposits. Interest earned in 4 year= 10000(1+0.05)^4 Interest earned in 5 year= 10000(1+0.05)^5 Ratio= {10000(1.05)^4}/{10000(1.05^5)} =&gt;1.05^4/1.05^5 =&gt;1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105 Hence Ans:100:105 <result>C</result>

C

KODAK bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?

aqua_rat__0g30N9pOQK9ZBKoU

Virat buys an old car for Rs. 60000 and spends Rs. 4000 on its repairs. If he sells the scooter for Rs. 65000, his gain percent is: Choose one A) 3 (4/7) % B) 11 (1/9) % C) 12 (2/3) % D) 1.6% E) None of these

Explanation: C.P. = Rs. (60000 + 4000) = Rs. 64000 S.P. = Rs. 65000. Gain% = ( (1000 / 64000) * 100 ) % = 1.6% ANSWER 1.6% <result>D</result>

D

Virat buys an old car for Rs. 60000 and spends Rs. 4000 on its repairs. If he sells the scooter for Rs. 65000, his gain percent is:

aqua_rat__L9jysYZddYJU3jl8

Of the 800 employees of Company X, 30 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 20 percent ? Choices: A) 200 B) 160 C) 112 D) 80 E) 100

The # oflong-termemployees is 30%*800=240. After y of them retire new # oflong-termemployees would become 240-y. Total # of employees would become 800-y. We want 240-y to be 20% of 800-y --&gt; 240-y=(800 -y)*20% --&gt; y = 100. Answer: 100. <result>E</result>

E

Of the 800 employees of Company X, 30 percent have been with the company for at least ten years. If y of theselong-termmembers were to retire and no other employee changes were to occur, what value of y would reduce the percent oflong-termemployees in the company to 20 percent ?

aqua_rat__Ovm958BSVRrPOO9l

A solution of 90 litres contains milk and water in the ratio 7:x. If ten litres of water is added to the solution, the ratio becomes 3:2, find the value of x? Pick one: A) 2 B) 1.5 C) 3.5 D) 2.5 E) 3

Exp. Total new quantity = original sol + water =90+10= <gadget id="calculator">90+10</gadget> <output>100</output> 100 New ratio= 3:2, New quantity of milk =3/5*100= <gadget id="calculator">3/5*100</gadget> <output>60</output> 60 Lit, New quantity of water= 2/5*100= <gadget id="calculator">2/5*100</gadget> <output>40</output> 40 Lit Water present initially= (40-10)= <gadget id="calculator">(40-10)</gadget> <output>30</output> 30 Lit Ratio= 60/30 =7/x There for x = 3.5 Answer: 3.5 <result>C</result>

C

A solution of 90 litres contains milk and water in the ratio 7:x. If ten litres of water is added to the solution, the ratio becomes 3:2, find the value of x?

aqua_rat__zk4g5CB3YNhHBCve

A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $70. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard) Select the correct option A) 70xy B) 630xy C) xy/9 D) xy/70 E) 630/(xy)

xy sq ft = $70 1 sq ft = $70/xy multiplying by 9 on both side 9 sq ft = $630/xy or 1 sq yard = $630/xy Hence 630/(xy). <result>E</result>

E

A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $70. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)

aqua_rat__R9vXmCmSq1J3R2u9

A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling? Pick. A) 620 km/hr B) 220 km/hr C) 220 km/hr D) 120 km/hr E) 203 km/hr

Explanation: Number of gaps between 41 poles = 40 So total distance between 41 poles = 40*50= <gadget id="calculator">40*50</gadget> <output>2_000</output> 2000 meter= 2 km In 1 minute train is moving 2 km/minute. Speed in hour = 2*60= <gadget id="calculator">2*60</gadget> <output>120</output> 120 km/hour Answer: 120 km/hr <result>D</result>

D

A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?

aqua_rat__kK8dfOUUgu6yYETZ

An investor deposited $10,000 to open a new savings account that earned 8 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened? Choices: A) $10,200 B) $10,202 C) $10,400 D) $10,404 E) $10,800

The amount in the account after 6 months is 1.02*1.02($10,000) = $10,404. The answer is $10,404. <result>D</result>

D

An investor deposited $10,000 to open a new savings account that earned 8 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?

aqua_rat__4NEjsD7X78lEcLPX

Find the odd man out. 30, -5, -45, -90, -145, -195, -255 Choose the correct choice from the following choices A) -145 B) -195 C) -30 D) -90 E) -5

30 30 - 35 = -5 -5 - 40 = -45 -45 - 45 = -90 -90 - 50 = -140 -140 - 55 = -195 -195 - 60 = -255 Hence, -145 is wrong. -140 should have come in place of -145 -145nswer is -145 <result>A</result>

A

Find the odd man out. 30, -5, -45, -90, -145, -195, -255

aqua_rat__Rx3nKQnSGr93M2u3

How many positive integers less than 8,000 are there in which the sum of the digits equals 5? Pick: A) 57 B) 56 C) 55 D) 54 E) 53

Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread. Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators). So, for example: XX|X|X|X = 2111 ||XXX|XX = 0032 etc. There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56. 56 <result>B</result>

B

How many positive integers less than 8,000 are there in which the sum of the digits equals 5?

aqua_rat__sH9UWJUkdz2l8NL6

In a deck of cards there are 50 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it? Pick one: A) 1/4. B) 4/17. C) 5/29. D) 8/31. E) 1/3.

4+12 tens/50+12 total cards=16/62=8/31 8/31. <result>D</result>

D

In a deck of cards there are 50 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?

aqua_rat__gGAHb9fsQdYTGgLR

If x is a whole number, then x²(x² - 1) is always divisible by Choose one: A) 12-x B) Multiple of 12 C) 12 D) 24 E) 48

Putting x = 2,we get 2²(2² - 1) = 12. checking with other integers, the above equation always gives a value which is a multiple of 12, So, x²(x² - 1) is always divisible by 12. ANSWER:12 <result>C</result>

C

If x is a whole number, then x²(x² - 1) is always divisible by

aqua_rat__u3Suih2YyDWyFcPE

The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's? Choices. A) 2.3 B) 2.5 C) 3.5 D) 3.6 E) 4.6

Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)] = 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20. Required average = (9.2 / 2) = 4.6. 4.6 <result>E</result>

E

The average of 6 no.'s is 3.95. The average of 2of them is 3.4, while the average of theother 2 is 3.85. What is the average of the remaining 2 no's?

aqua_rat__M4UFoYSYYE2IZE84

AB +BA ___ 121 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B? Choose the most appropriate option. A) 6 B) 8 C) 9 D) 11 E) 14

two ways to do it.. 1) straight logic.. we can see that ones digit is 1 when units digit B and A are added.. answer has to be 1 in the units digit.. only 11 fits in.. 2) BA=10B+A, and AB=10A+B.. it is given that BA+AB=121.. or 10B+A +10A+B=121.. 11(A+B)=121.. so A+B=11.. ANSWER:11 <result>D</result>

D

AB +BA ___ 121 In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?

aqua_rat__XD2iKibf77sG6k2L

Calculate the average mark scored by Adam if he had the following scores in an examination: 86, 75, 72, 63 and 65 marks (out of 100) in French Language, Geography, Art and design, History and Physical Education respectively? Pick: A) 39.2 B) 79.2 C) 72.2 D) 71.2 E) 76.2

Explanation: Average mark = 86+75+72+63+65/5=72.2 Answer: Option 72.2 <result>C</result>

C

Calculate the average mark scored by Adam if he had the following scores in an examination: 86, 75, 72, 63 and 65 marks (out of 100) in French Language, Geography, Art and design, History and Physical Education respectively?

aqua_rat__POy5dHuanSgeRuWv

Light glows for every 15 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am. Choose the correct option: A) 380 times B) 381 times C) 382 times D) 392 times E) 331 times

Time difference is 1hr,22min,49sec=4969sec. So, light glows floor(4969/15)=331 times. ANSW331 timesR:331 times <result>E</result>

E

Light glows for every 15 seconds . How many max. times did it glow between 1:57:58 and 3:20:47 am.

aqua_rat__PAWZzcFdCKuRCxzD

If both 5^3 and 3^4 are factors of n x (2^5) x (12^2) x (7^3) x (10^2), what is the smallest possible positive value of n? Choose the correct choice from the following answers: A) 15 B) 45 C) 75 D) 125 E) 150

(2^5) x (12^2) x (7^3) x (10) has two appearances of 3 (in 12^2) and two appearances of 5 (in 10^2). Thus n must include at least 3^2 * 5 = 45 The answer is 45. <result>B</result>

B

If both 5^3 and 3^4 are factors of n x (2^5) x (12^2) x (7^3) x (10^2), what is the smallest possible positive value of n?

aqua_rat__S9nnrWRzkZQxrnJk

In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is? Choose the most appropriate option A) 5320 B) 5325 C) 5330 D) 5334 E) 5336

Divisor = (5 * 46)= <gadget id="calculator">(5 * 46)</gadget> <output>230</output> 230= 10 * Quotient = Divisor =&gt; Quotient = 230/10= <gadget id="calculator">230/10</gadget> <output>23</output> 23 Dividend= (Divisor * Quotient) + Remainder Dividend = (230 * 23) + 46= <gadget id="calculator">(230 * 23) + 46</gadget> <output>5_336</output> 5336 5336) <result>E</result>

E

In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 46, the dividend is?

aqua_rat__fQ7ssJWXS5RJSn0a

Suppose, the speed of any positive integer n is defined as follows: seed(n) = n, if n < 10 = seed(s(n)), otherwise, where s(n) indicates the sum of digits of n.For example, seed(7) = 7, seed(248) = seed(2 + 4 + 8) = seed(14) = seed(1 + 4) = seed(5) = 5 etc. How many positive integers n, such that n < 500, will have seed (n) = 9? Options: A) 39 B) 72 C) 81 D) 108 E) 55

Explanation : We need to find out numbers less than 500, with sum of digits as 9. We know that a number will be divisible by 9, if the sum of its digits is divisible by 9. For eg : 18 has sum of digits 9. 198 has sum of digits 18, which has its sum of digits 9. So, we need to find numbers less than 500 which are divisible by 9, or are multiples of 9 i.e 500/9 is 55.5555. Hence, there are 55 numbers which are multiples of 9 less than 500. Answer : 55 <result>E</result>

E

Suppose, the speed of any positive integer n is defined as follows: seed(n) = n, if n < 10 = seed(s(n)), otherwise, where s(n) indicates the sum of digits of n.For example, seed(7) = 7, seed(248) = seed(2 + 4 + 8) = seed(14) = seed(1 + 4) = seed(5) = 5 etc. How many positive integers n, such that n < 500, will have seed (n) = 9?

aqua_rat__IIYCiDnFw90YkhZR

What is the smallest integer that satisfies the inequality ((x - 3)/ (x^2 - 8x - 20)) > 0? Choose the most appropriate option A) -2 B) 10 C) -1 D) 3 E) 0

Let us factorize the denominator and rewrite the expression as (x−3)/((x−10)(x+2))&gt; 0 Equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good. The values that are relevant to us are x = 3, x = 10 and x = -2. Let us arrange these values in ascending order: -2, 3 and 10. The quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals. Interval 1: x &lt; -2. Pick a value in that range and check whether the inequality holds good. Let us take x = -10. When x = -10, (x−3)/((x−10)(x+2))&lt; 0; the inequality DOES NOT hold good in this interval. Interval 2: -2 &lt; x &lt; 3. Let us take x = 0. When x = 0, (x−3)/((x−10)(x+2)) = (0−3)/((0−10)(0+2)) &gt; 0; the inequality holds good in this interval. The least integer value that x can take if x &gt; -2 is x = -1. ANSWER : -1. <result>C</result>

C

What is the smallest integer that satisfies the inequality ((x - 3)/ (x^2 - 8x - 20)) > 0?

aqua_rat__VFCCZ44keYizDFHh

Eight children — A, B, C, D, E, F, G and H — are going to sit in eight chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children? Options. A) 600 B) 720 C) 10080 D) 14320 E) 14800

for such questions , we can treat both as one then total person=7.. these 7 can be arranged in 7! ways.. but within these 7 , one consists of two people who can be arranged in 2 ways CF or FC.. so ans =7!*2=10080 ans 10080 <result>C</result>

C

Eight children — A, B, C, D, E, F, G and H — are going to sit in eight chairs in a row. The children C & F have to sit next to each other, and the others can sit in any order in any remaining chairs. How many possible configurations are there for the children?

aqua_rat__ux01RooAo14v4Awo

Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio D of men to women? Options. A) 5:2 B) 5:1 C) 4:3 D) 4:1 E) 3:1

(5:2) D=184 x 5 + 170 x 2 = 1260.5:2 <result>A</result>

A

Students at a school were on average 180 cm tall. The average female height was 170 cm, and the average male height was 184 cms. What was the ratio D of men to women?

aqua_rat__ZqyynSXh1Bdwrg4o

A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 73 marks. The maximum marks are? Choose the correct choice from the following answers: A) 450 B) 300 C) 500 D) 600 E) 175

Let the maximum marks be x Then, 33% of x = 125+73 33x/100 = 198 x = 600 Answer is 600 <result>D</result>

D

A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 73 marks. The maximum marks are?

aqua_rat__9sCR8zogt1Sbyr5t

Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. five years from today, the difference between the age of the boy and the combined ages of the girls will be Choose the correct choice from the following answers: A) 1 B) 2 C) -4 D) –2 E) –1

Approach I (Plugin's) Girl I ............... Girl II ................ Boy 1 ....................... 1 ........................ 3 (Assume the current ages) 1 + 1 &lt; 3 .......... (Satisfies the given condition) 1 Year later there ages are 2 ....................... 2 ......................... 4 2 + 2= <gadget id="calculator">2 + 2</gadget> <output>4</output> 4 ............ (Satisfies the given condition) After 5 years there ages are 6 ....................... 6 ............................ 8 Difference= 8 - (6+6) = 8 - 12 = -4 Answer = -4 <result>C</result>

C

Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. five years from today, the difference between the age of the boy and the combined ages of the girls will be

aqua_rat__Dc2ng86McSFyteVd

Two trains are traveling towards the same direction. First train is moving at speed of 100 km/hour and second train 200 km/hour.When will the head of first train start overtaking the second train. Choose the correct choice from the following answers: A) 2 hour B) 1 hour C) 2.5 hour D) 3.5 hour E) 4 hour

Difference between the speed of two trains 750 – 500 = 250 km. In 60 minutes, the second train reduces the gap from the first train by 100 km. So, to reduce the gap of 250 km, the train will take 180 minutes or 2.5 hours. Answer: 2.5 hour. <result>C</result>

C

Two trains are traveling towards the same direction. First train is moving at speed of 100 km/hour and second train 200 km/hour.When will the head of first train start overtaking the second train.

aqua_rat__Tf2C6rXMnIOTqnxb

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is? Choose the correct choice from the following answers A) 100 B) 272 C) 287 D) 189 E) 289

4/3 π * 10 * 10 * 10 = 8 * 4/3 πr3 r = 5 4π * 5 * 5 = 100π 100nswer:1004 * 5 * 5= <gadget id="calculator">4 * 5 * 5</gadget> <output>100</output> 100π 100nswer:100 <result>A</result>

A

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in cm2) is?

aqua_rat__gVkvCfou055EvTHY

Jim is now twice as old as Fred, who is nine years older than Sam. Six years ago, Jim was five times as old as Sam. How old is Jim now? Pick: A) 42 B) 46 C) 50 D) 54 E) 58

J = 2F = 2(S+9) = 2S+18 J-6 = 5*(S-6) (2S+18)-6 = 5S-30 S = 14 and so J = 46 The answer is 46. <result>B</result>

B

Jim is now twice as old as Fred, who is nine years older than Sam. Six years ago, Jim was five times as old as Sam. How old is Jim now?

aqua_rat__bXq6YohDNygeWnec

A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey? Choose the correct choice: A) 11 B) 24 C) 55 D) 66 E) 71

Distance from A and B be 'd' Average Speed = total distance/total time Average Speed = (2d)/[(d/20) + (d/30)] = (2d)/[5d/60) =&gt; 24 kmph. Answer: 24 <result>B</result>

B

A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?

aqua_rat__TxmoRRfvmdLHGrUK

12 : 8 seconds :: ? : 4 minutes Pick: A) 10 B) 15 C) 6 D) 8 E) 7

12*4=8*x x=6 ANSWER:6 <result>C</result>

C

12 : 8 seconds :: ? : 4 minutes

aqua_rat__NyBMsz170qfkzm7x

) A cube is painted blue on all of its surfaces. It is then cut in to 27 smaller cubes of equal size. Find how many smaller cubes have no color? Choose the correct choice from the following: A) 1 B) 3 C) 8 D) 5 E) 7

If the cube is cut in to 27 smaller cubes, then number of separations made = n = 3 (since 3×3×3=27). Number of smaller cubes with no color = (n–2)3 = (3–2)3 = 13 = 1 1nswer:1 <result>A</result>

A

) A cube is painted blue on all of its surfaces. It is then cut in to 27 smaller cubes of equal size. Find how many smaller cubes have no color?

aqua_rat__dwNQCrw5DfcnAkP2

A train 700 m long can cross an electric pole in 40 sec and then find the speed of the train? Choose the most appropriate option: A) 987 B) 271 C) 72 D) 27 E) 63

Length = Speed * time Speed = L/T S = 700/40= <gadget id="calculator">700/40</gadget> <output>35/2 = around 17.5</output> 17.5 M/Sec Speed= 17.5*18/5 (To convert M/Sec in to Kmph multiply by 18/5) Speed = 63 Kmph Answer:63 <result>E</result>

E

A train 700 m long can cross an electric pole in 40 sec and then find the speed of the train?

aqua_rat__eem2VLzvG3gDl4j4

Find the least number must be subtracted from 964807 so that remaining no.is divisible by 8? Select: A) 7 B) 6 C) 5 D) 4 E) 3

On dividing 964807 by 15 we get the remainder 7, so 7 should be subtracted 7 <result>A</result>

A

Find the least number must be subtracted from 964807 so that remaining no.is divisible by 8?

aqua_rat__RAaONHuTLCE4AIxl

In 1995 a certain store had 1,800 tools in stock that had been purchased for $30 each. If 1,000 of these tools were sold in 1995 for $50 each and the remaining 800 were sold in 1996 for $60 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995? Choose the correct answer: A) $0 B) $4,000 C) $8,000 D) $32,000 E) $40,000

The keyword here isGross Profit: Gross Profit = (Selling Price - Original Price)*(# of Items Sold) So lets figure out what the Gross Profit for 1995: GP1995 = (50-30)*(1000)= <gadget id="calculator">(50-30)*(1000)</gadget> <output>20_000</output> 20000 And the Gross Profit for 1996: GP1996= (60-30)*(800)= <gadget id="calculator">(60-30)*(800)</gadget> <output>24_000</output> 24000 So the difference would be: 24000-20000= <gadget id="calculator">24000-20000</gadget> <output>4_000</output> 4000 ANSWER: B. 4000 <result>B</result>

B

In 1995 a certain store had 1,800 tools in stock that had been purchased for $30 each. If 1,000 of these tools were sold in 1995 for $50 each and the remaining 800 were sold in 1996 for $60 each, how many greater was the gross profit on the tools sold in 1996 than the gross profit on those sold in 1995?

aqua_rat__S9BPeo0E05pgt3mc

What is the exact probability that, when rolling six fair dice, at least one of the dice shows a 6? Choose the most appropriate option: A) 1 B) 31031/46656 C) 5/6 D) 35625/46656 E) 1/6

For each dice, the probability of not rolling a 6 is 5/6. The total probability of not rolling a 6 is (5/6)^6. The correct answer is thus 1 - (5/6)^6 = 31031/46656, so the answer is 31031/46656. <result>B</result>

B

What is the exact probability that, when rolling six fair dice, at least one of the dice shows a 6?

aqua_rat__FeycuDUzvu1TDI1E

A family pays $900 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much? Choose the correct choice from the following choices: A) $1,000 B) $1,200 C) $1,400 D) $1,500 E) $1,700

Assuming the medical expenses are $1000 or more, the family pays $900 + $400 = $1300. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $700 when the medical expenses are $1700. The answer is $1,700.900 + 400= <gadget id="calculator">900 + 400</gadget> <output>1_300</output> $1300. The total amount paid by insurance plan for the first $1000 of expenses is $600. The insurance will pay another $700 when the medical expenses are $1700. The answer is $1,700. <result>E</result>

E

A family pays $900 per year for an insurance plan that pays 60 percent of the first $1,000 in expenses and 100 percent of all medical expenses thereafter. In any given year, the total amount paid by the family will equal the amount paid by the plan when the family's medical expenses total how much?

aqua_rat__sVCFVahZ90aXsIRH

The sum of ages of 5 children born 3 years different each is 50 yrs. What is the age of the Elder child? Choices: A) 10 B) 12 C) 16 D) 19 E) 20

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 x = 4. x+12= 4+12= <gadget id="calculator">4+12</gadget> <output>16</output> 16 16 <result>C</result>

C

The sum of ages of 5 children born 3 years different each is 50 yrs. What is the age of the Elder child?

aqua_rat__eQIpaIgSBjKVmjQ1

65% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets? Select: A) (a) 15% B) (b) 5% C) (c) 10% D) (d) 20% E) (e) 25%

so 35% employees don't have VCD devices. 25% employees don't have MO 20% employees don't have ACs 15% employees don't have WM Summ of employees that don't have some device = 35%+25%+20%+15% = 95% &lt; 100% So definitely at least 5% employees have 4 devices. ans: (b) 5%35 +25 +20 +15= <gadget id="calculator">35 +25 +20 +15</gadget> <output>95</output> 95% &lt; 100% So definitely at least 5% employees have 4 devices. ans: (b) 5% <result>B</result>

B

65% of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?

aqua_rat__yf3asAC8MzJPY7Oq

Insert the missing number. 2, 6, 12, 20, 30, 42, (....) Pick one. A) 56 B) 38 C) 72 D) 66 E) 19

Explanation: The pattern is 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7 So, the next number is 7 x 8 = 56. 56nswer: 56) 56 <result>A</result>

A

Insert the missing number. 2, 6, 12, 20, 30, 42, (....)

aqua_rat__pPYxwHGrvwT4f6Wj

A person traveled 3 equal distances 20km/hr, 30km/hr, 60km/hr then find its avg speed? Choose the correct choice from the following. A) 20km/hr B) 30km/hr C) 22km/hr D) 19km/hr E) 31km/hr

avg speed = 3xyz/(xy+yz+zx) required answer is = 3*20*30*60/ (600+1800+1200)= <gadget id="calculator">3*20*30*60/ (600+1800+1200)</gadget> <output>30</output> 30km/hr Answer is 30km/hr <result>B</result>

B

A person traveled 3 equal distances 20km/hr, 30km/hr, 60km/hr then find its avg speed?

aqua_rat__VYmEM7lXuLn77SJX

How many minutes will be used to cover distance of 520m, if a man running at the speed of 15km/hr? Options: A) 125 sec B) 124 sec C) 114 sec D) 115 sec E) 117 sec

Explanation: Distance = time × speed = 125 sec. 125 secnswer: 125 sec <result>A</result>

A

How many minutes will be used to cover distance of 520m, if a man running at the speed of 15km/hr?

aqua_rat__QUiONmd7OvSnMHDW

A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 6 hours, then the distance covered at 40 kmph is Choose the correct choice. A) 220 km B) 120km C) 100km D) 140km E) none of these

Let the partial distance covered at 40 kmph be X Let the another partial distance covered at 60 kmph be (250 - x) Thus, x/40 - (250 - x)/60 = 6 or, x/40 + (250 - x)/60 = 6 or, (3x + 500 - 2x)//120 = 6 or 500 + x = 720 x=220 220 kmNSWER:220 km <result>A</result>

A

A bus covered a distance of 250 km, partly at an average speed of 40 kmph and partly at 60 kmph. If the total time taken is 6 hours, then the distance covered at 40 kmph is

aqua_rat__rCk72RAZX019XhuO

A and B can do a piece of work in 30 days and 30 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed? Choose the most appropriate option: A) 30days B) 35days C) 40days D) 45days E) 50days

Explanation: (30days+B)’s 10 days work = 10[1/30+1/30]=10[1+1/30]= 2/3 30days complete remaining work in 2/3*30= <gadget id="calculator"> 2/3*30</gadget> <output>20</output> 20 Total work= 10+20= <gadget id="calculator">10+20</gadget> <output>30</output> 30days 30daysnswer: Option 30days <result>A</result>

A

A and B can do a piece of work in 30 days and 30 days respectively. They work together for 10 days and B leaves. In how many days the whole work is completed?

aqua_rat__22UIbm2NBAWWpIx6

A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount. How much amount B have. Answers. A) 83.5% B) 87.5% C) 88.5% D) 89.5% E) Rs 484

Explanation: In this type of question, we will first try to calculate the ratio of two persons. Once we get ratio then we can easily get our answer. So lets solve this. 4/15A=2/5B A=(2/5∗14/4)B A=3/2B A/B=3/2 A:B=3:2 B's Share = 2/5∗1210=484 Option Rs 484 <result>E</result>

E

A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount. How much amount B have.

aqua_rat__0gn8Ib10L1jsXWp2

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long? Choose the most appropriate option: A) 40 B) 99 C) 77 D) 66 E) 32

Speed = 45 * 5/18 = 25/2 m/sec Total distance covered = 360 + 140= <gadget id="calculator">360 + 140</gadget> <output>500</output> 500 m Required time= 500 * 2/25= <gadget id="calculator">500 * 2/25</gadget> <output>40</output> 40 sec 40nswer: 40 <result>A</result>

A

A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?

aqua_rat__TMGwplNCT3Hv27Vf

What are the last two digits of 36*28*61*83*73*62? Choose the correct choice from the following options A) 11 B) 09 C) 07 D) 05 E) 04

36*28*61*83*73*62= We have to focus on the last two digits only, so 36*28=08*61=88*83=04 04*73=92 therefore 92*62=04 Hence Answer is 04 <result>E</result>

E

What are the last two digits of 36*28*61*83*73*62?

aqua_rat__SVSHV7NsbvIEoEaL

The overall age of X and Y is 11 year greater than the overall age of Y and Z. Z is how many decades younger that X? Choose the correct choice from the following answers A) 11 B) 15 C) 12 D) 17 E) 19

11 11 (X + Y) – (Y + Z) = 11 X – Z = 11 <result>A</result>

A

The overall age of X and Y is 11 year greater than the overall age of Y and Z. Z is how many decades younger that X?

aqua_rat__eDYvf74f7Duerl0R

If x = 2^8 and x^x = 2^k, what is k? Choose the correct choice from the following choices. A) 2^15 B) 2^14 C) 2^13 D) 2^12 E) 2^11

Solution: We know that x=2^8 which implies x^x = (2^8)^(2^8) = 2^(8 * 2^8) [because (x^y)^z = x^(y*z))] so 2^(2^3 * 2^8) = 2^(2^(3+8)) [because x^a * x^b = x^(a+b)] therefore x^x = 2^(2^11) Given that x^x=2^k so 2^(2^11) = 2^k Since the base is same the exponent will also be same therefore k = 2^11 Answer: 2^11 <result>E</result>

E

If x = 2^8 and x^x = 2^k, what is k?

aqua_rat__pzkxLLSLcwAY880E

A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? Choose the correct answer. A) 90 B) 52 C) 63 D) 87 E) 10

Explanation: Let number of notes of each denomination be x. Then x + 5x + 10x = 480 16x = 480 x = 30. Hence, total number of notes = 3x = 90. 90nswer:90 <result>A</result>

A

A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?

aqua_rat__p2C8dlMvjoT04T9y

The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches? Select: A) 66 B) 83.5 C) 84 D) 95 E) 76

sum of last 4 matches = (10 × 66) – (6 × 54)= 336 Average = 336/4= <gadget id="calculator">336/4</gadget> <output>84</output> 84 ANSWER:84 <result>C</result>

C

The averge score of a cricketer for ten matches is 66 runs. If the average for the first six matches is 54. Then find the average for the last four matches?

aqua_rat__N7mTd9sSLwgDVyuN

Two persons starting from the same place walk at a rate of 8kmph and 15kmph respectively. What time will they take to be 14 km apart, if they walk in the same direction? Choose one. A) 7 hrs B) 2 hrs C) 5 hrs D) 12 hrs E) 6 hrs

The relative speed of the boys = 15kmph – 8kmph = 7 kmph Distance between them is 8.5 km Time= 14km / 7 kmph =2 hrs Answer : 2 hrs <result>B</result>

B

Two persons starting from the same place walk at a rate of 8kmph and 15kmph respectively. What time will they take to be 14 km apart, if they walk in the same direction?

aqua_rat__jhABw27OIEOQQGRJ

17 times a positive integer is more than its square by 70, then the positive integer is Choose the correct choice from the following options: A) 13 B) 10 C) 11 D) 12 E) 14

Explanation: Let the number be x. Then, 17x = x2 + 70 =&gt; x2 - 17x + 70 = 0 =&gt;(x - 7)(x - 10) = 0 =&gt; x = 7 or 10 Answer: 10 <result>B</result>

B

17 times a positive integer is more than its square by 70, then the positive integer is

aqua_rat__GDjLqhvxBZhVsB6t

A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 18 sec. What is the length of the platform? Choose the most appropriate option. A) 288 B) 350 C) 889 D) 276 E) 234

Speed = 300/18 = 50/3 m/sec. Let the length of the platform be x meters. Then, (x + 300)/39 = 50/3 3x + 900 = 1950 =&gt; x = 350 m. Answer:350 <result>B</result>

B

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

aqua_rat__qeAGF7acP0O91znZ

If log 2 = 0.3010 and log 3 = 0.4771, the values of log5 512 is Choose the correct choice from the following A) 3.879 B) 3.875 C) 3.872 D) 3.828 E) 3.192

ANS: log5512 = {\color{3.875lack} \frac{\log 512}{\log 5}} = {\color{3.875lack} \frac{\log 2^{9}}{\log (\frac{10}{2})}} ={\color{3.875lack} \frac{9\log 2}{\log10-\log 2 }} ={\color{3.875lack} \frac{(9\times 0.3010)}{1-0.3010 }} ={\color{3.875lack} \frac{2.709}{0.699 }} ={\color{3.875lack} \frac{2709}{699 }} =3.876 Answer: 3.875) 3.875 <result>B</result>

B

If log 2 = 0.3010 and log 3 = 0.4771, the values of log5 512 is

aqua_rat__Okd1jNTk5PCj59jP

A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at? Answers A) 12 min B) 16 min C) 18 min D) 15 min E) 19 min

Since A and B move in the same direction along the circle, so they will first meet each other when there is a difference of one round between the two. Relative speed of A and B = 6 - 1= <gadget id="calculator">6 - 1</gadget> <output>5</output> 5 rounds per hour. Time taken to complete one round at this speed= 1/5 hr = 12 min. 12 minnswer:12 min <result>A</result>

A

A walks around a circular field at the rate of one round per hour while B runs around it at the rate of six rounds per hour. They start in the same direction from the same point at 7.30 a.m. They shall first cross each other at?

aqua_rat__THeyW21PP8skKiy9

If .005^4 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain? Choose the correct choice from the following. A) 0 B) 8 C) 9 D) 10 E) 11

0.005^4= (5*10^-3)^4 = 625*10^-12 = 0.625*10^-9 which would have 9 zeros to the right of the decimal point. The answer is 9. <result>C</result>

C

If .005^4 is represented in its shortest possible decimal form, how many 0’s to the right of the decimal point does it contain?

aqua_rat__x8jaE6tZ5tuReFD1

A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at: Choose the correct answer: A) 4.6% B) 3.6% C) 6.4% D) 7.8% E) 8.9%

C 6.4% Income from $ 4000 at 5 % in one year = $ 4000 of 5 %. = $ 4000 × 5/100. = $ 4000 × 0.05. = $ 200. Income from $ 3500 at 4 % in one year = $ 3500 of 4 %. = $ 3500 × 4/100. = $ 3500 × 0.04. = $ 140. Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340. Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340. = $ 160. Total invested amount = $ 4000 + $ 3500 = $7500. Remaining invest amount = $ 10000 - $ 7500 = $ 2500. We know that, Interest = Principal × Rate × Time Interest = $ 160, Principal = $ 2500, Rate = r [we need to find the value of r], Time = 1 year. 160 = 2500 × r × 1. 160 = 2500r 160/2500 = 2500r/2500 [divide both sides by 2500] 0.064 = r r = 0.064 6.4%hange it to a percent by moving the decimal to the right two places r = 6.4 % Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year. <result>C</result>

C

A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at:

aqua_rat__LsmrJ3a220La12OG

If three distinct positive divisors of 64 are randomly selected, what is the probability that their sum will be less than 32? Choose the correct choice from the following options: A) 1/3 B) 1/2 C) 2/7 D) 10/21 E) 15/28

The positive divisors are 1, 2, 4, 8, 16, 32, 64. If any of the first five are chosen, the sum will be less than 32. P(sum is less than 32) = 5/7 * 4/6 * 3/5 = 12/42 = 2/7 The answer is 2/7. <result>C</result>

C

If three distinct positive divisors of 64 are randomly selected, what is the probability that their sum will be less than 32?

aqua_rat__GCehkheSeYIiFFsg

A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m? Choose the correct answer. A) 29798 B) 27908 C) 78902 D) 25000 E) 27000

27 * 2 * 0.75 = 20/100 * 10/100 * 7.5/100 * x 27 = 1/100 * x =&gt; x = 27000 Answer: 27000 <result>E</result>

E

A brick measures 20 cm * 10 cm * 7.5 cm how many bricks will be required for a wall 27 m * 2 m * 0.75 m?

aqua_rat__isjGrq60OBxmkwo6

A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is? Choose the correct choice from the following options: A) 238 B) 150 C) 988 D) 210 E) 171

Let the length of the train be x m and its speed be y m/sec. Then, x/y = 15 =&gt; y = x/15 (x + 140)/25 = x/15 =&gt; x = 210 m. Answer: 210 <result>D</result>

D

A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is?

aqua_rat__D8C8dyUbF399bWp7

A certain number of machines can do a work in 100days. If there were 10 machines more it could be finished in 10days less. How many machines are there? Choose the correct answer: A) 50 B) 40 C) 90 D) 100 E) 60

Original number of machines = 10 * (100-10)/10= <gadget id="calculator">10 * (100-10)/10</gadget> <output>90</output> 90 machines Answer is 90 <result>C</result>

C

A certain number of machines can do a work in 100days. If there were 10 machines more it could be finished in 10days less. How many machines are there?

aqua_rat__0baN8g8j414yrOlY

For which of the following functions f is f(y) = f(1-y) for all y? Choose the correct choice from the following choices. A) f (x) = 1 - x B) f (x) = 1 - x^2 C) f (y) = y^2 - (1 - y)^2 D) f (y) = y^2*(1 - y)^2 E) f (y) = y/(1 - y)

I remember seeing this problem in a GMATprep test. I think choice D should be F(y)=(y^2) (1-y)^2. If that is true then substituting (1-y) for will give us the same function back and the answer choice is f (y) = y^2*(1 - y)^2, where the function is multiplicative <result>D</result>

D

For which of the following functions f is f(y) = f(1-y) for all y?

aqua_rat__8tFb2nPrTQaRYRo4

The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#27? Options: A) 6 B) 7 C) 8 D) 9 E) 10

First, let's translate the expression 21#27, using the definition given: 21#27 = 21×24×27 We need the prime factorization of this product. Let's factor out 3 from each multiple. 21#27 = 3^3(7×8×9) Now let's replace each consecutive integer with its prime factorization: 21#27 = 3^3(7×2^3×3^2) Let's group the prime bases: 21#27 = 2^3×3^5×7 The sum of the exponents is 3 + 5 + 1= <gadget id="calculator"> 3 + 5 + 1</gadget> <output>9</output> 9 The answer is 9. <result>D</result>

D

The expression x#y denotes the product of the consecutive multiples of 3 between x and y, inclusive. What is the sum of the exponents in the prime factorization of 21#27?

aqua_rat__HoUpriOvM5uTQcJX

A rectangular floor is covered by a rug except for a strip 3 meters wide along each of the four edge. If the floor is 12 meters by 10 meters, what is the area of the rug in square meters? Answers. A) 30 B) 28 C) 36 D) 42 E) 24

A strip of 3 meters is covering the inner rectangular rug for all 4 sides. Length of inner rug = 12-(2*3) breadth of inner rug= 10-(2*3) Area of Rug= 6 * 4= <gadget id="calculator">6 * 4</gadget> <output>24</output> 24 sq. mt Ânswer: 24 <result>E</result>

E

A rectangular floor is covered by a rug except for a strip 3 meters wide along each of the four edge. If the floor is 12 meters by 10 meters, what is the area of the rug in square meters?

aqua_rat__BdUELuMzX4pPcQFL

Of the diplomats attending a summit conference, 14 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference? Choices A) 72 B) 96 C) 108 D) 120 E) 180

{Total} = {French} + {Russian} - {Both} + {Neither} {Total} = 14 + ({Total} - 32) - (0.1*{Total}) + 0.2*{Total} Solving gives {Total} = 180. Answer: 180. <result>E</result>

E

Of the diplomats attending a summit conference, 14 speak French, 32 do not speak Russian, and 20% of the diplomats speak neither French nor Russian. If 10% of the diplomats speak both languages, then how many diplomats attended the conference?

aqua_rat__z5unh4E7iccHtTBf

Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 9 on the two dice? Choose the most appropriate option: A) 4/9 B) 5/9 C) 7/18 D) 11/18 E) 7/36

There are 36 possible outcomes for two dice. The number of outcomes with an even number on the first die is 3*6= <gadget id="calculator">3*6</gadget> <output>18</output> 18. The number of outcomes with a sum of 9 is 4. We need to subtract the outcomes that have both an even number on the first die and a sum of 9 because we have counted those outcomes twice. This number of outcomes is 2. The number of outcomes with either an even number on the first die or a sum of 9 is 18+4-2= <gadget id="calculator"> 18+4-2</gadget> <output>20</output> 20. The probability is 20/36=5/9. The answer is 5/9. <result>B</result>

B

Two dice are tossed once. What is the probability of getting an even number on the first die or a total sum of 9 on the two dice?

aqua_rat__CX51oLRgVXyQ5afo

The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream? Choose the correct choice A) 16 kmph B) 18 kmph C) 14 kmph D) 79 kmph E) 27 kmph

The ratio of the times taken is 2:1. The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1)= <gadget id="calculator">(2+1)/(2-1)</gadget> <output>3</output> 3/1= <gadget id="calculator">3/1</gadget> <output>3</output> 3:1 Speed of the stream= 42/3= <gadget id="calculator">42/3</gadget> <output>14</output> 14 kmph. Answer: 14 kmph <result>C</result>

C

The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?

aqua_rat__uLawLsBZDiU4haqD

A's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ? Choose the correct choice: A) 10 B) 20 C) 30 D) 40 E) 50

10'S sal = 40% of B =40% Of (25% of C) = 40/100(25/100*100) % Of C = 10% 10NSWER 10 <result>A</result>

A

A's salary is 40% of B's salary which is 25% of C's salary. What percentage of C's salary is A's salary ?

aqua_rat__TtzHjKjwWHhnVOAt

An article is bought for Rs.560 and sold for Rs.340, find the loss percent? Select: A) 36% B) 38% C) 16% D) 39% E) 12%

560 ---- 220 100 ---- ? =&gt; 39% Answer:39% <result>D</result>

D

An article is bought for Rs.560 and sold for Rs.340, find the loss percent?

aqua_rat__d0BzinC7sEUioLRX

Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 4 of the slips are the drawn, without replacement, what is the probability that all 4 have a odd number written on it? Choose the correct option: A) 1/12 B) 1/10 C) 1/8 D) 1/42 E) 5/9

Key is that there is no replacement, so each successive choice will become more skewed towards picking a neg (i.e. the pool of positives decreases, while the pool of negatives stay the same) P(+ on 1st pick) = 5/10 P(+ on 2nd pick) = 4/9 P(+ on 3rd pick) = 3/8 P(+ on 4rd pick) = 2/7 5/10*4/9*3/8*2/7=1/42 1/42 <result>D</result>

D

Each of the integers from 0 to 9, inclusive, is written on a separate slip of blank paper and the ten slips are dropped into a hat. If 4 of the slips are the drawn, without replacement, what is the probability that all 4 have a odd number written on it?

aqua_rat__FsZz0lX5wiz1DkU1

A chemical tank of capacity 2000m3 which is 65% full is found to be leaking. The chemical in the tank needs to be transported to a new destination using tanker trucks. If the capacity of a truck is 16m3 which can be filled upto 93% full. How many truck loads would be needed to transport the chemical? Select A) 64 B) 71 C) 85 D) 92 E) 97

Volume of chemical in the tank=2000x0.65=1300 Volume of the truck=16x.93=15.36 Number of truck loads needed= 1300/15.36=84.63≈85 Answer: 85 <result>C</result>

C

A chemical tank of capacity 2000m3 which is 65% full is found to be leaking. The chemical in the tank needs to be transported to a new destination using tanker trucks. If the capacity of a truck is 16m3 which can be filled upto 93% full. How many truck loads would be needed to transport the chemical?

aqua_rat__74niX8FmRY6iy7oh

The average of 65 numbers is 40. If two numbers, 79 and 60 are discarded, then the average of the remaining numbers is nearly Answers: A) 28.32 B) 39 C) 38.78 D) 39.06 E) 30

Explanation : Total sum of 63 numbers = (65*40) - (79 +60) = 2600 - 139= <gadget id="calculator">2600 - 139</gadget> <output>2_461</output> 2461 Average= 2457/63 = 39.06 Answer : 39.06 <result>D</result>

D

The average of 65 numbers is 40. If two numbers, 79 and 60 are discarded, then the average of the remaining numbers is nearly

aqua_rat__212FmtahfWoLjZKc

If x+y=10z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z? Choose the correct choice from the following answers: A) 4z-1 B) 3z C) 5z D) z/3 E) 3z/2

Pick any number like X=12, Y=18 and Z= 3 so that X+Y=10Z, now then the arithmetic mean will be (12+18+3)/3= <gadget id="calculator"> (12+18+3)/3</gadget> <output>11</output> 11. Now, just look at the answers and put the value of Z there. (4z-1) 4.3-1=11,it can be the answer, lets check us the other options (B) 3.3=6, no (C) 5.3=15, no (D) 3/3, no (E) (3.3)/2=3, no so the answer will be 4z-1.. <result>A</result>

A

If x+y=10z, then which of the following represents the average (arithmetic mean) of x, y, and z, in terms of z?

aqua_rat__CHom0jnBdCXaSUyR

In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is theprobability that the extracted ball would turn onto be white, if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ? Choose the correct choice from the following A) 3/5 B) 5/8 C) 6/7 D) 7/8 E) 6/7

Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag. ∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4] = 1/4 [(4 + 3 + 2 + 1)/4] = 5/8 5/8 <result>B</result>

B

In a bag containing 3balls, a white ball was placed and then 1ball was taken out at random. What is theprobability that the extracted ball would turn onto be white, if all possible hypothesisconcerning the color of the balls that initially in the bag were equally possible ?

aqua_rat__cEvBhaDpkkmuQIdH

A train 125 m long passes a man, running at 10 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is? Choose the most appropriate option: A) 65 km/hr B) 17 km/hr C) 55 km/hr D) 50 km/hr E) 15 km/hr

Speed of the train relative to man = 125/10 = 25/2 m/sec. = 25/2 * 18/5= <gadget id="calculator">25/2 * 18/5</gadget> <output>45</output> 45 km/hr Let the speed of the train be x km/hr. Then, relative speed= (x - 10) km/hr. x - 10 = 45 =&gt; x = 55 km/hr. Answer: 55 km/hr <result>C</result>

C

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

aqua_rat__3BJO2Cos8P8KEVKj

Factor | Percent of Respondents | User-friendly | 56% | Fast response time | 48% | Bargain prices | 42% | The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,400 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?” Choose the correct choice from the following. A) 312 B) 336 C) 364 D) 384 E) 420

The way I looked at is is as follows: UserFriendly(UF) + FastResponse (FR) = 30% UF leftover = 56 - 30= <gadget id="calculator">56 - 30</gadget> <output>26</output> 26% FR leftover= 48 - 30= <gadget id="calculator">48 - 30</gadget> <output>18</output> 18% Sum these= 74% (ie. 74% were either UF+FR, UF, FR) 26% leftover is the maximum number for Bargain Price 26/100 * 1400 = 26 * 14= <gadget id="calculator">26 * 14</gadget> <output>364</output> 364 (364). <result>C</result>

C

Factor | Percent of Respondents | User-friendly | 56% | Fast response time | 48% | Bargain prices | 42% | The table gives three factors to be considered when choosing an Internet service provider and the percent of the 1,400 respondents to a survey who cited that factor as important. If 30 percent of the respondents cited both “user-friendly” and “fast response time,” what is the maximum possible number of respondents who cited “bargain prices,” but neither “user-friendly” nor “fast response time?”

aqua_rat__Qn1tSzHOrdNJzowN

A man is trying to climb over a frozen mountain that is sixty feet high. Every minute, he can climb 3 feet, but due to the slippery ice, he slips back 2 feet. How long will it take him to reach the top of the mountain? Choose the correct choice: A) 57 minutes B) 58 minutes C) 59 minutes D) 53 minutes E) 54 minutes

Solution: It will take the man 58 minutes to reach the top. Since he is climbing 3 feet and falling 2 feet back every passing minute, he is actually climbing 1 feet every minute. Therefore, he would have climbed 57 feet in 57 minutes. The remaining distance is 3 feet. He will take one more minute to climb it and reach the surface. Since he has reached the top surface, he won't slip back. 58 minutes Answer 58 minutes <result>B</result>

B

A man is trying to climb over a frozen mountain that is sixty feet high. Every minute, he can climb 3 feet, but due to the slippery ice, he slips back 2 feet. How long will it take him to reach the top of the mountain?

aqua_rat__s7rgEFp1piHOiJAR

The decimal d is formed by writing in succession all the positive, odd integers in increasing order after the decimal point; that is d = 0.1357911131517... What is the 100th digit of d to the right of decimal point? Choose the correct choice. A) 5 B) 1 C) 0 D) 9 E) 7

One-digit odd numbers: There are (1)(10/2) = 5 odd one-digit numbers. 0.13579 5 digits down, 95 remaining. The next 5 odd numbers will be 11, 13, 15, 17, and 19, ... so it follows that: (2)(5) = 10 digits. Two-digit numbers: 90 digits, which brings us to the number 99. Three-digit numbers: we only need 5 more digits. The next odd numbers are 101, and 103, thus 0 is the 100th digit. Answer: 0 <result>C</result>

C

The decimal d is formed by writing in succession all the positive, odd integers in increasing order after the decimal point; that is d = 0.1357911131517... What is the 100th digit of d to the right of decimal point?

aqua_rat__iNYAiFUWeVIjfZXp

There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 68% Choices: A) 14.11 B) 19.75 C) 20.75 D) 21.75 E) 22.75

60*84/100= <gadget id="calculator">60*84/100</gadget> <output>252/5 = around 50.4</output> 50.40 lit milk that is 9.60 lit water let x lit water will be added then (60+x)*68/100=50.40 so x=14.11 14.11NSWER:14.11 <result>A</result>

A

There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 68%

aqua_rat__X4kQHHzZf7sUqTSJ

A sum of money lent out at S.I. amounts to a total of $520 after 2 years and to $820 after a further period of 5 years. What was the initial sum of money that was invested? Select: A) $340 B) $360 C) $380 D) $400 E) $420

S.I for 5 years = $820 - $520 = $300 The S.I. is $60/year S.I. for 2 years 820 - 520= <gadget id="calculator">820 - 520</gadget> <output>300</output> $300 The S.I. is $60/year S.I. for 2 years= $120 Principal = $520 - $120 = $400 The answer is $400.520 - 120= <gadget id="calculator">520 - 120</gadget> <output>400</output> $400 The answer is $400. <result>D</result>

D

A sum of money lent out at S.I. amounts to a total of $520 after 2 years and to $820 after a further period of 5 years. What was the initial sum of money that was invested?

aqua_rat__Vd3SuINMUSs5Gzuj

A cricket bat is sold for $850, making a profit of $215. The profit percentage would be Choose one. A) 24% B) 25% C) 34% D) 36% E) 40%

215/(850 - 215) = 215/635 = 43/127 =34%. Answer: 34%. <result>C</result>

C

A cricket bat is sold for $850, making a profit of $215. The profit percentage would be

aqua_rat__JmRcq97rgQYeo27p

A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? Choose the most appropriate option: A) 18:11 B) 18:16 C) 18:10 D) 18:14 E) 14:11

A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only. 18:11 : B 8000*18 : (8000*4) + (4000*14) 14400 : 88000 18:11:B = 18:11 18:11nswer: 18:11 <result>A</result>

A

A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?

aqua_rat__nakSCxDauNoJDflW

You are gifted a coin that is dated 378 B.C. How much worth the coin is as per your assumption? Choose the correct choice from the following choices A) 1 B) 0 C) 2 D) 5 E) 6

Solution: The worth of that coin is zero. This is because the B.C. and A.D. dating system was not empowered till the year 525. So the coin is probably fake. Answer 0 <result>B</result>

B

You are gifted a coin that is dated 378 B.C. How much worth the coin is as per your assumption?

aqua_rat__yfNOwoU9vGbLWoUT

Dustin's Pizza Shop sells 3 sizes of pizza: Small, Medium, and Large. A Small pizza contains 4 slices, A Medium Pizza contains 6 slices and a Large pizza contains 10 slices. Lisa, a customer having a birthday party, visits the shop with her 2 daughters and 9 friends. To ensure each of the visitors receive an equal amount of pizza with none leftover, which of the following combinations are possible? Choose the correct choice from the following answers: A) 1 Small and 1 Large B) 4 Small and 1 Medium C) 2 Small and 4 Medium D) 4 Medium and 1 Large E) 1 Medium and 3 Large

There are 12 total customers (Lisa, 2 daughters, and 9 friends) The correct combination must be divisible by 12 with no remainder. A= 14 Slices (1 slice per guest with 2 slices leftover) B= 22 Slices (1 Medium and 3 Largeach kid would have 2 slices, but Lisa would have none) C= 32 Slices (8 visitors would have 3 slices, but 4 visitors would only have 2) D= 34 Slices (10 Visitors would have 3 slices, but 2 visitors would only have 2) 1 Medium and 3 Large= 36 Slices (1 Medium and 3 Largeach visitor would have 3 slices, with nothing leftover) *Correct Answer* The Correct Answer is 1 Medium and 3 Large <result>E</result>

E

Dustin's Pizza Shop sells 3 sizes of pizza: Small, Medium, and Large. A Small pizza contains 4 slices, A Medium Pizza contains 6 slices and a Large pizza contains 10 slices. Lisa, a customer having a birthday party, visits the shop with her 2 daughters and 9 friends. To ensure each of the visitors receive an equal amount of pizza with none leftover, which of the following combinations are possible?

aqua_rat__62vl357OKyh7JEuT

If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=0 ii. u is not equal to v iii.u > v Choose one: A) None B) I only C) II only D) III only E) II and III

Notice two things: 1. we are asked to find out which of the following MUST be true, not COULD be true and 2. s, u, and v are positive integers. Given: 2s=2u+2v --&gt; s=u+v. Now, since s, u, and v are positive integers then s is more than either u or v, so I is never true and III is always true. As for II: it's not necessarily true, for example 4=2+2. . Nonenswer: None <result>A</result>

A

If s,u, and v are positive integers and 2s=2u+2v, which of the following must be true? i. s=0 ii. u is not equal to v iii.u > v

aqua_rat__sq2s6zBH3KyXENuG

Which of the following equations describes a line that is perpendicular to y = x/2 + 6? Choose the correct answer. A) y = x − 6 B) y = −1 − 2x C) y = -3x D) y = 6x-1 E) y = 1/x + 6

Two perpendicular lines have slopes that are inverse reciprocals of each other. The slope of y = x/2 + 6 is 1/2 so the slope of a perpendicular line will be -2. The answer is y = −1 − 2x. <result>B</result>

B

Which of the following equations describes a line that is perpendicular to y = x/2 + 6?

aqua_rat__31iQngy63deIwihc

Three friends had dinner at a restaurant. When the bill was received, Amita paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Tanya paid. What faction of the bill did Veena pay ? Choose the correct choice from the following: A) 1/3 B) 3/11 C) 12/13 D) 5/8 E) 9/8

let veena paid x, so anita paid 2/3 x, and tanya paid 2x, so total bill paid is given by x+(2/3)x +2x = 1 i.e. x=3/11 ANSWER:3/11 <result>B</result>

B

Three friends had dinner at a restaurant. When the bill was received, Amita paid 2/3 as much as Veena paid and Veena paid 1/2 as much as Tanya paid. What faction of the bill did Veena pay ?

aqua_rat__rRCKkxIII1vr5uPa

40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim? Choose the correct choice from the following options: A) 60 B) 70 C) 80 D) 90 E) 100

Given, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks. Given, marks of Robert = 80 30% of 80 = 30/100 * 8 = 24 Given, 40% of Ram's marks = 24. =&gt; Ram's marks = (24 * 100)/40= <gadget id="calculator">(24 * 100)/40</gadget> <output>60</output> 60 Also, 20% of Rahim's marks= 24 =&gt; Rahim's marks = (24 * 100)/20= <gadget id="calculator">(24 * 100)/20</gadget> <output>120</output> 120 Average marks of Ram and Rahim= (60 + 120)/2= <gadget id="calculator">(60 + 120)/2</gadget> <output>90</output> 90. ANSWER:90 <result>D</result>

D

40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?

aqua_rat__XGECvVJ6y6Xhi9dj

An Olympic diver received the following scores: 7, 4, 8, 10, and 6. The standard deviation of her scores is in which of the following ranges? Choose the correct choice from the following options. A) 0-1.9 B) 2-3.9 C) 4 – 6.9 D) 7 – 7.9 E) 8 – 9.9

7+4+8+10+6/5 =7 | 7-7= <gadget id="calculator"> 7-7</gadget> <output>0</output> 0 0^2= 0 |4-7| = 3^2 = 9 | 8-7= <gadget id="calculator"> 8-7</gadget> <output>1</output> 1^2=1 | 10-7= <gadget id="calculator"> 10-7</gadget> <output>3</output> 3^2= 9 |6-7| = 1^2 = 1 SD = sqrt 20/5 = 2 Answer : 2-3.9 <result>B</result>

B

An Olympic diver received the following scores: 7, 4, 8, 10, and 6. The standard deviation of her scores is in which of the following ranges?

aqua_rat__cdiMKIfw7zLfQrmj

A 10-by-7 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed? Choose the correct choice. A) The volume of the cylinder with height 10 is 70/pi cubic inches greater than the volume of the cylinder with height 6. B) The volume of the cylinder with height 7 is 70/pi cubic inches greater than the volume of the cylinder with height 10. C) The volume of the cylinder with height 10 is 70pi cubic inches greater than the volume of the cylinder with height 6. D) The volume of the cylinder with height 7 is 70pi cubic inches greater than the volume of the cylinder with height 10. E) The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 7 and 10 are the circumference of the base and not the radius. The volume of the cylinder with height 7 is 70/pi cubic inches greater than the volume of the cylinder with height 10. is the right answer. <result>B</result>

B

A 10-by-7 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

aqua_rat__tffgsMQldTTjXn3I

In how many different ways can 7 girls and 7 boys form a circle such that the boys and the girls alternate? Choose the correct choice from the following: A) 2880211 B) 3628800 C) 120000 D) 36286200 E) None of these

Explanation : In a circle, 7 boys can be arranged in 6! ways Given that the boys and the girls alternate. Hence there are 7 places for girls which can be arranged in 7! ways Total number of ways = 6! x 7! = 720 x 5040 = 3628800. Answer : Option 3628800 <result>B</result>

B

In how many different ways can 7 girls and 7 boys form a circle such that the boys and the girls alternate?

aqua_rat__e1tOtAd1Fg3RwuuR

On 8th march,2005,Wednesday falls. What day of the week was it on 8th march,2004? Choices. A) 28 B) 00 C) 27 D) 01 E) 8

Answer:01 <result>D</result>

D

On 8th march,2005,Wednesday falls. What day of the week was it on 8th march,2004?

aqua_rat__Sl23dUPRJhISjEfW

Two employees X and Y are paid a total of Rs. 638 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week? Pick: A) s.250 B) s.280 C) s.290 D) s.299 E) s.300

Let the amount paid to X per week = x and the amount paid to Y per week = y Then x + y = 638 But x = 120% of y = 120y/100 = 12y/10 ∴12y/10 + y = 638 ⇒ y[12/10 + 1] = 638 ⇒ 22y/10 = 638 ⇒ 22y = 6380 ⇒ y = 6380/22 = 580/2 = Rs.290 s.290 <result>C</result>

C

Two employees X and Y are paid a total of Rs. 638 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?