mathewhe/aqua_rat huggingface dataset:
Question: If YWVSQ is 25 - 21 - 21 - 19 - 17, Then MKIGS
(A) 13 - 11 - 9 - 7 - 9
(B) 13 - 11 - 6 - 7 - 6
(C) 13 - 11 - 9 - 7 - 7
(D) 13 - 11 - 9 - 7 - 3
(E) 13 - 11 - 9 - 7 - 1
Rationale: MKIGS = 13 - 11 - 6 - 7 - 6
Note: this is a dummy question. Dont answer these questions
Answer:B
Answer: (B) 13 - 11 - 6 - 7 - 6
Question: Consider a square of diagonal length d. Let Another square be formed with d as its side. Find the ratio of the area of the bigger square to that of the smaller square.
(A) 2
(B) 3
(C) 4
(D) 16
(E) 41
Rationale: d^2/(1/2)*d^2= 2
ANSWER:A
Answer: (A) 2
Question: The length of the bridge, which a train 100 metres long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) 10 m
(B) 16 m
(C) 275 m
(D) 19 m
(E) 27 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (100 + x)/30
= 25/2 => 2(100 + x) = 750 => x
= 275 m.
Answer: C
Answer: (C) 275 m
Question: If a randomly selected positive single digit multiple of 3 is multiplied by a randomly selected prime number less than 20, what is the probability T that this product will be a multiple of 45?
(A) 1/32
(B) 1/28
(C) 1/24
(D) 1/16
(E) 1/14
Rationale: There are 3 single digit multiple of 3, that is, 3,6,9.
There are 8 prime nos less than 20 - 2,3,5,7,11,13,17,19
Total outcome - 8*3 = 24
Favourable outcome = 1 (9*5)
Hence required probability T= 1/24. Answer C.
Answer: (C) 1/24
Question: 1,3,5,7,9,..50 find term of sequnce for this?
(A) 1368
(B) 1457
(C) 1567
(D) 1478
(E) 2500
Rationale: This is an arithmetic progression, and we can write down
a=1a=1 ,d=2d=2 , n=50n=50 .
We now use the formula, so that
Sn=12n(2a+(n−1)l)Sn=12n(2a+(n−1)l)
S50=12×50×(2×1+(50−1)×2)S50=12×50×(2×1+(50−1)×2)
=25×(2+49×2)=25×(2+49×2)
=25×(2+98)=25×(2+98)
=2500=2500.
E
Answer: (E) 2500
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
(A) 12.9 kmph
(B) 18.9 kmph
(C) 28.9 kmph
(D) 12.5 kmph
(E) 27.8 kmph
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b)
= 4 and 45/(a + b) + 40/(a - b)
= 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D
Answer: (D) 12.5 kmph
Question: The manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.75 $ each, 4 sodas at 1.50 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold?
(A) 1.48$
(B) 1.58$
(C) 1.60$
(D) 1.63$
(E) 1.70$
Rationale: For every 10 tickets amount of snacks sold is 3*2.75+4*1.5+2*1=$16.25, hence amount of the snacks sales per ticket is $16.25/10=~$1.63.
Answer: D.
Answer: (D) 1.63$
Question: Find the one which does not belong to that group ?
(A) 3
(B) 4
(C) 5
(D) 8
(E) 6
Rationale: Explanation:
3, 5, 9 and 7 are odd numbers, but not 4.
Answer: B
Answer: (B) 4
Question: A cistern which could be filled in 6 hours takes one hour more to be filled owing to a leak in its bottom. If the cistern is full in what time will the leak empty it?
(A) 76 hrs
(B) 99 hrs
(C) 15 hrs
(D) 90 hrs
(E) 11 hrs
Rationale: 1/6 - 1/x = 1/10
=> 15 hrs
Answer: C
Answer: (C) 15 hrs
Question: A 1400 m long train crosses a tree in 100 sec, how much time will It take to pass a platform 700 m long?
(A) 288
(B) 190
(C) 150
(D) 188
(E) 12
Rationale: L = S*T
S= 1400/100
S= 14 m/Sec.
Total length (D)= 2100 m
T = D/S
T = 2100/14
T = 150 Sec
Answer:C
Answer: (C) 150
Question: A university cafeteria offers 6 flavors of pizza - pork,gobi-manjurian,pepperoni, chicken, Hawaiian and vegetarian. If a customer has an option (but not the obligation) to add extra cheese, mushrooms or both to any kind of pizza, how many different pizza varieties are available ?
(A) 4
(B) 8
(C) 12
(D) 36
(E) 32
Rationale: 6 flavours * 6 choices = 6C1*6C1 = 6*6=36=D
Answer: (D) 36
Question: You are renting an apartment and you need √625 for each side, how many feet are you looking to measure?
(A) 21
(B) 22
(C) 23
(D) 24
(E) 25
Rationale: Try filling the numbers into the answer y x y =
Find the closest to 625.
Answer E
Answer: (E) 25
Question: Find the HCF of 54, 288, 360
(A) 18
(B) 36
(C) 54
(D) 108
(E) None of these
Rationale: Explanation:
Lets solve this question by factorization method.
18=2×32,288=25×32,360=23×32×5
So HCF will be minimum term present in all three, i.e.
2×32=18
Answer: Option A
Answer: (A) 18
Question: Find the odd man out. 187, 264, 386, 473, 682, 781
(A) 187
(B) 386
(C) 781
(D) 682
(E) 473
Rationale: In all numbers except 386, the middle digit is the sum of other two digits.
Answer is B
Answer: (B) 386
Question: 3 numbers are randomly selected, with replacement, from the set of integers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If the first number selected is w, the second number selected is x, and the third number is y, what is the probability that w < x < y ?
(A) 3/40
(B) 28/243
(C) 3/25
(D) 33/100
(E) 64/125
Rationale: Solution:
Total possible ways = 10*10*10 = 1000
Case1: w=0.
if x = 1, then y can have 8 ways.
if x =2 , then y can have 7 ways and so on.
So, no. of ways = 8+7+..+1
Case2 : w=1.
if x = 2, then y can have 7 ways.
if x =3 , then y can have 6 ways and so on.
So, no. of ways = 7+6 +..+1
There will be 8 cases in this way and they will follow a pattern which looks like this:
No. of ways for Case1 : 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8
No. of ways for Case2 : 1 + 2 + 3 + 4 + 5 + 6 + 7
No. of ways for Case3 : 1 + 2 + 3 + 4 + 5 + 6
No. of ways for Case4 : 1 + 2 + 3 + 4 + 5
No. of ways for Case5 : 1 + 2 + 3 + 4
No. of ways for Case6 : 1 + 2 + 3
No. of ways for Case7 : 1 + 2
No. of ways for Case8 : 1
____________________________________________________________
Total number of ways : 8(1) + 7(2) + 6(3) + 5(4) + 4(5) + 3(6) + 2(7) + 1(8) = 2(4(5) + 3(6) + 2(7) + 1(8)) = 2(60) = 120
Therefore, ans is 120/1000 = 3/25.
Option c.
Answer: (C) 3/25
Question: Which of the following is(are) true for a@b=b@a?
I. a@b=ab+a
II. a@b=(a+b)(a-b)
III. a@b=(a/b)+(b/a)
(A) only Ⅰ
(B) only Ⅱ
(C) only Ⅲ
(D) only ⅠⅢ
(E) only ⅡⅢ
Rationale: -> If I. a@b=ab+ba, a@b=ab+ba=ba+ab=b@a (O).
If II. a@b=(a+b)(a-b), a@b=(a+b)(a-b)≠(b+a)/(b-a)=b@a (O).
If III.a@b=(a/b)+(b/a), a@b=(a/b)+(b/a)=(b/a)+(a/b)=b@a (X).
Thus, ⅠⅢ are the answers. Therefore, E is the answer.
Answer: (E) only ⅡⅢ
Question: In the new budget the price of milk rose by 10%. By how much percent must a person reduce his consumption so that his expenditure on it does not increase?
(A) 7.5%
(B) 9.1%
(C) 10.9%
(D) 12.6%
(E) 15%
Rationale: Reduce in consumption = R/(100+R) *100% = 10/110 *100 = 9.1%
Answer is C
Answer: (C) 10.9%
Question: xy+yx=46xy+yx=46 Find x & y values ?
(A) 45
(B) 878
(C) 66
(D) 88
(E) 01
Rationale: l: 145+451=46145+451=46
Hence x = 1, y = 45
AnswerA
Answer: (A) 45
Question: What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30?
(A) 228
(B) 630
(C) 998
(D) 267
(E) 212
Rationale: L.C.M of 12, 18, 21, 30
= 2 * 3 * 2 * 3 * 7 * 5 = 1260
Required number = 1260/2 = 630.
Answer:B
Answer: (B) 630
Question: a,b,c,d,e sitting in a row what is the probability that a & b sitting adjacent.
(A) 1/5
(B) 2/5
(C) 3/5
(D) 4/5
(E) 6/5
Rationale: total number of arrangement is= 5!= 120
Favorable event i.e a and b can be arranged in 2! and the remaining can be arranged in 4! since ab can be in any of the four positions.
so 4!*2!/5! = 2/5
ANSWER:B
Answer: (B) 2/5
Question: Solve the equation 2 – x = 2b – 2ax, where a and b are real parameters. Find for which values of a the equation has for solution a natural number, if b = 7
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Solution:
We write the given equation like this (2a - 1)x = 2(b - 1)
The following cases are possible:
If 2a - 1 ≠ 0, i.e. a ≠ 1/2, the equation has single solution
x = 2(b - 1)/(2a - 1)
If a = 1/2 and b = 1, the equation gets the kind 0.x = 0 and every x is solution
If a = 1/2 and b ≠ 1, we get 0.x = 2(b - 1), where 2(b - 1) ≠ 0
In this case the equation has no solution.
If b = 7 and a ≠ 1/2 the single solution is
x = 2(7 - 1)/(2a - 1) = 12/(2a - 1)
If a is whole number, then 2a - 1 is also whole number and the solution
x = 12/(2a - 1) is natural number when
2a - 1 is positive divisor of 12.
To have a as whole number, the divisor of 12 mu be odd.But the only whole positive odd numbers divisible by 12 are 1 and 3.
Therefore 2a - 1 = 3 <=> a = 2 or 2a - 1 = 1 <=>
a = 1 a = 2 or 2a - 1 = 1 <=> a = 1
Answer B
Answer: (B) 1
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is?
(A) 25/42
(B) 25/49
(C) 25/46
(D) 25/48
(E) 35/49
Rationale: Total fruits = 9
Since there must be at least two apples,
(⁵C₂ * ⁴C₁)/⁹C₃ + ⁵C₃/⁹C₃
= 25/42.
Answer:A
Answer: (A) 25/42
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
(A) 18 days
(B) 12 days
(C) 24 days
(D) 10 days
(E) 15 days
Rationale: Explanation:
8/12 + 6/x = 1
X = 18 days
Answer: A
Answer: (A) 18 days
Question: Which of the following is the sum of all the even numbers between 3 and 99, inclusive?
(A) 2550
(B) 2449
(C) 2600
(D) 2499
(E) 2652
Rationale: 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...
4+96 = 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 = 100
46+54 = 100
48+52 = 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+50-1 = 2449
Final Answer:
B
Answer: (B) 2449
Question: If Tim had lunch at $50.20 and he gave 20% tip, how much did he spend?
(A) $30.60
(B) $60.60
(C) $70.60
(D) $40.60
(E) $60.24
Rationale: The tip is 20% of what he paid for lunch. Hence
tip = 20% of 50.20 = (20/100)*50.20 = $10.04
Total spent
50.20 + 10.04 = $60.24
correct answer E
Answer: (E) $60.24
Question: Before 5 years, dog A’s age was 4 times of dog B’s age and after 4 years, dog A’s age will be 3 times of dog B’s age. What is the difference of dog A’s age and dog B’s now?
(A) 36
(B) 42
(C) 58
(D) 60
(E) 64
Rationale: A - 5 = 4(B - 5) --> A - 4B = -15.............1
A + 4 = 3(B + 4) --> A - 3B = 8.............2
(2) - (1) --> B = 23 --> A =3(27)=81
A - B = 81 - 23 = 58
Answer: C
Answer: (C) 58
Question: when x is diveded by 299 remainder is 100. then when x is divided by 23 remainder is ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: 299+100=399=>x
399/23 gives a remainder of 8
ANSWER:E
Answer: (E) 8
Question: Edward has $732,391 dollars in his savings account. What is the least amount of money (in whole number of dollars) that he must add from his account if he wants to split this money evenly among his nine children?
(A) $1
(B) $2
(C) $3
(D) $4
(E) $5
Rationale: In order to divide the sum in 9 parts, the amount must be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 732,391 = 25 and 27 is divisible by 9.
Hence we need to add 2 to this number for it to be divisible by 9
Correct Option: B
Answer: (B) $2
Question: In a group of 28 junior high school students, 7 take French, 10 take Spanish, and 4 take both languages. The students taking both French and Spanish are not counted with the 7 taking French or the 10 taking Spanish. How many students are not taking either French or Spanish?
(A) 7
(B) 6
(C) 9
(D) 4
(E) 8
Rationale: A
7
Add 7 + 10 + 4 to get 21.
Then subtract 21 from the total students ⇒ 28 – 21 = 7.
Answer: (A) 7
Question: What will be the reminder when (43^43+43) is divided by 44?
(A) 32
(B) 42
(C) 83
(D) 71
(E) 92
Rationale: (x^n+1) will be divisible by (x+1) only when n is odd;
(43^43+1) will be divisible by (43+1);
(43^43+1)+42 when divided by 44 will give 42 as remainder.
Correct Option : B
Answer: (B) 42
Question: An article is bought for Rs.680 and sold for Rs.900, find the gain percent?
(A) 33 1/8%
(B) 33 8/3%
(C) 33 1/3%
(D) 32 6/17%
(E) 32 1/3%
Rationale: 680---- 220
100 ---- ? => 32 6/17%
Answer: D
Answer: (D) 32 6/17%
Question: A box contains eight bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly two bulbs are good?
(A) 3/7
(B) 17/35
(C) 19/35
(D) 16/35
(E) 18/35
Rationale: Required probability = (4C2 . 4C2)/8C4 = (6 * 6)/70
= 18/35
Answer:E
Answer: (E) 18/35
Question: Skier Lindsey Vonn completes a straight 300-meter downhill run in t seconds and at an average speed of (x + 10) meters per second. She then rides a chairlift back up the mountain the same distance at an average speed of (x - 8) meters per second. If the ride up the mountain took 135 seconds longer than her run down the mountain, what was her average speed, in meters per second, during her downhill run?
(A)  10
(B)  15
(C)  20
(D)  25
(E)  30
Rationale: Backsolving is the preferred approach for this one
300/(x-8) - 300/(x+10) = 135
We are asked for the value of x+10
So we can start with C = X+10 = 20
So x = 10
300/2 - 300 / 20 = 135
Hence answer is C
Answer: (C)  20
Question: At a certain supplier, a machine of type A costs $23,000 and a machine of type B costs $50,000. Each machine can be purchased by making a 20 percent down payment and repaying the remainder of the cost and the finance charges over a period of time. If the finance charges are equal to 40 percent of the remainder of the cost, how much less would 2 machines of type A cost than 1 machine of type B under this arrangement?
(A) $5,280
(B) $11,200
(C) $12,000
(D) $12,800
(E) $13,200
Rationale: Total Cost of 2 Machines of Type A
= 20% of (Cost of 2 machine A) + remainder + 40 % remainder
= 20% of 46000 + (46000 - 20% of 46000) + 40% of (46000 - 20% of 46000)
= 60720
Total Cost of 1 Machine of Type B
= 20% of (Cost of 1 machine B) + remainder + 40 % remainder
= 20% of 50000 + (50000 - 20% of 50000) + 40% of (50000 - 20% of 50000)
= 66000
Diff = 66000 - 60720 = 5280
Hence, A.
Answer: (A) $5,280
Question: If the numerator of a fraction is increased by 20% and its denominator is diminished by 25% value of the fraction is 2/15. Find the original fraction.
(A) 1/12
(B) 1/8
(C) 1/6
(D) 1/4
(E) 1/5
Rationale: Explanation:
X * (120/100)
---------------- = 2/15
Y * (75/100)
X/Y = 1/12
ANSWER IS A
Answer: (A) 1/12
Question: Fred and Frank are partners in a business. Frank runs the business and for this he gets 7% of the profit , and the rest is divided in proportion to their capitals. If Frank invested 15000 and Fred invested 35000, find the share of Frank in a profit of 10000.
(A) 1166.7
(B) 2266.7
(C) 2766.7
(D) 2466.7
(E) 6766.7
Rationale: The amount Frank gets for managing
= 7% of Rs. 10000 = 700
Remaining profit = 10000 â€“ 700 = 9300
This is to be divided in the ratio 10000:35000=10: 35=2:7
Share of Frank = 2/9 of 9300 = 2066.7
â‡’ Total share of Frank = 700 + 2066.7 = 2766.7.
Answer C
Answer: (C) 2766.7
Question: Mukesh weight 56.7 kg. If he reduces his weight in the ratio 7:6. New weight of Mukesh is ?
(A) 47.6
(B) 48.6
(C) 49.6
(D) 50.6
(E) 51.6
Rationale: Given ratio is 7:6;
let weight before and after reduction be 7x and 6x respectively.
A/Q
7x=56.7
=> x=56.7/7
=> x= 8.1
Reduced weight= 6x= 6*8.1= 48.6;
hence reduced weight= 48.6
ANSWER:B
Answer: (B) 48.6
Question: Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 13 years older than Larry, how old is Annie?
(A) 6
(B) 8
(C) 19
(D) 26
(E) 34
Rationale: J = L+13
(1) 2(A+3) = L+3
(2) 3(A+5) = J+5 = L+18
Let's subtract equation (1) from equation (2)
A+9 = 15
A = 6
The answer is A.
Answer: (A) 6
Question: The sum of all two digit numbers divisible by 8 is
(A) 910
(B) 510
(C) 611
(D) 616
(E) 810
Rationale: Required numbers are 16,24 . . . . . 96
This is an A.P. in which a=16,d=8 and l=96.
Let the number of terms in it be n.Then t=96
So a+(n-1)d=96.
16+(n-1)*8=96
16+8n-8=96
8+8n=96
8n=96-8
n = 88/8
then n=11.
Required sum
=n/2(a+l)
=11/2(16+96)
=616
Answer is D
Answer: (D) 616
Question: Last year’s receipts from the sale of greeting cards during the week before Mother’s Day totaled $240 million, which represented 12 percent of total greeting card sales for the year. Total greeting card sales for the year totaled how many million dollars?
(A) 2,010
(B) 2,000
(C) 2,890
(D) 2,701
(E) 2,100
Rationale: 12% ---- 240 millions
for 100% => ( 240 * 100% )/12% = 2000.
Option B.
Answer: (B) 2,000
Question: I chose a number and divide it by 5. Then I subtracted 154 from the result and got 6. What was the number I chose?
(A) 800
(B) 700
(C) 900
(D) 1000
(E) 750
Rationale: Let x be the number I chose, then
x5−154=6
x5=160
x=800.
So answer is A.
Answer: (A) 800
Question: For positive integer x, if the sum of all the digit of x is 170 where x and y are positive integers and x=1020-y, which of the following can be the value of y?
(A) 41
(B) 47
(C) 50
(D) 55
(E) 60
Rationale: ->10^20-y=99999….9( )[ ] is derived.
In this case, the number of the first digits of 9 is 18, which is 9*18=162.
Also, the sum of all digits is 170.
That is, it should be ( )+[ ]=170-162=8.
Then, one should be selected amongst y=29,38,47,56,6,5,74,83,92.
Since 47 is in the option, the answer is B.
Answer: (B) 47
Question: Today Mary’s father is four times as old as Mary. Eight years ago, he was 12 times as old. How old is Mary today?
(A) 6
(B) 7
(C) 10
(D) 11
(E) 15
Rationale: Dad's age = 4M
12*(M-8) = 4M-8
8M = 88
M = 11
The answer is D.
Answer: (D) 11
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.64000?
(A) 81000
(B) 29899
(C) 26798
(D) 27799
(E) 27781
Rationale: 64000* 9/8 * 9/8 = 81000.Answer: A
Answer: (A) 81000
Question: 4,64,256,1024,...?
(A) 1096
(B) 2096
(C) 3096
(D) 4096
(E) 5096
Rationale: 4
4*16=64
4*64=256
4*256=1024
4*1024=4096
ANSWER:D
Answer: (D) 4096
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.84. How much was lent at 5%?
(A) 600
(B) 2998
(C) 277
(D) 500
(E) 271
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 84
5x/100 + 90 – 6x/100 = 84
x/100 = 6
=> x = 600.Answer: A
Answer: (A) 600
Question: A computer manufacturer produces a certain electronic component at a cost of $150 per component. Shipping costs for delivering the components are $1 per unit. Further, the manufacturer has costs of $19,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 250 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) 199
(B) 249
(C) 233
(D) 215
(E) 229
Rationale: $19500 is a fixed cost
Each component is $151 ($150 to produce, $1 to ship)
Manufacturer will be producing and selling 250 components
so therefore the equation to find price would be
250*p = 19500+(250*150)+(250*1)
p = (19500+37500+250)/250
p = 229
Answer: E
Answer: (E) 229
Question: Given a two-digit number, the unit's digit exceeds its ten's digit by 4 and the product of the given number and the sum of its digits is equal to 90, which of the options is the number?
(A) 26
(B) 15
(C) 37
(D) 62
(E) 73
Rationale: Using the elimination method the option that fits this description is 15
5-1 = 4 (unit's digit that exceeds its ten's digit by 4)
15*6 = 90 (the product of the given number and the sum of its digits is equal to 175)
answer :B
Answer: (B) 15
Question: 18 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
(A) 8 days
(B) 6 days
(C) 7 days
(D) 9 days
(E) 1 days
Rationale: 1 women's 1 day work = 1/126
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/126+ 10/140) = 1/9
5 women and 10 children will complete the work in 9 days.
Answer: D
Answer: (D) 9 days
Question: The LCM of three numbers is four times their GCF. Which of the following must be true of the numbers?
I. At least one of the numbers is odd.
II. Two of the three numbers must be same.
III. At least one number is the same as GCF.
(A) only
(B) option II only
(C) and III only
(D) and II only
(E) I and III only
Rationale: Consider the following set: {2, 4, 8}.
GCF = 2.
LCM = 8 = 4*2.
The set discards options I and II. Only B fits.
Answer: B.
Answer: (B) option II only
Question: In a class of 5 students, average weight of the 4 lightest students is 40 kgs, Average weight of the 4 heaviest students is 45 kgs. What is the difference between the the maximum and minimum possible average weight overall?
(A) 2.8 kgs
(B) 3.2 kgs
(C) 3 kgs
(D) 4 kgs
(E) 2 kgs
Rationale: DETAILED SOLUTION
If there are an odd number of terms, say, 2n + 1, then the median is the middle term. And if average is lesser than the middle term, there will at least be n + 1 terms greater than the average. So, there will be more terms above the average than below it.
However, this need not be the case when there are an even number of terms. When there are 2n distinct terms, n of them will be greater than the median and n will be lesser than the median. The average of these two terms can be such that there are n terms above the average and n below it.
For instance, if the numbers are 0, 1, 7, 7.5. The median is 4, average is 3.875. Average is less than the median. And there are more 2 numbers above the average and 2 below the average.
Correct Answer: Median is 4, average is 3.875.
Correct Answer: D
Answer: (D) 4 kgs
Question: A library has an average of 1000 visitors on Sundays and 700 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
(A) 740
(B) 750
(C) 760
(D) 770
(E) 775
Rationale: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (1000 * 5 + 700 * 25) / 30 = 22500/30 = 750
Answer: B) 750
Answer: (B) 750
Question: A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after 3 months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C?
(A) 4 : 9 : 8
(B) 5 : 7 : 4
(C) 6 : 10 : 7.5
(D) 7 : 9: 4
(E) 5 : 4 : 8
Rationale: Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 9) = 36 : 60 : 45
= 6 : 10 : 7.5.
ANSWER :C
Answer: (C) 6 : 10 : 7.5
Question: A student has to obtain 33% of the total marks to pass. He got 125 marks and failed by 40 marks. The maximum marks are?
(A) 450
(B) 300
(C) 500
(D) 610
(E) 175
Rationale: Let the maximum marks be x
Then, 33% of x = 125+40
33x/100 = 165
x = 500
Answer is C
Answer: (C) 500
Question: A total of 30 percent of the geese included in a certain migration study were male. If some of the geese migrated during the study and 10 percent of the migrating geese were male, what was the ratio of the migration rate for the male geese to the migration rate for the female geese? [Migration rate for geese of a certain sex = (number of geese of that sex migrating) / (total number of geese of that sex)]
(A) 1/4
(B) 7/12
(C) 2/3
(D) 7/27
(E) 8/7
Rationale: Let' take the Number of geese to be 100.
Male = 30. Female = 70.
Now the second part of the Q, Let's take the Number migrated to be 20.
So we have 20 geese that migrated and out of that 10% are male i.e 10/100 *20 = 2 Geese (Males)
And now we know out of the total 20 geese , 2 are male , then 18 have to be female.
Now the ratio part , Male Geese Ratios = 2/30 = 1/15. - A
Female Geese Ratios =18/70=9/35 - B
Cross Multiply Equations A and B and you get = 7/27.
Ans D
Answer: (D) 7/27