mathewhe/aqua_rat huggingface dataset:
Question: How many unique positive odd integers less than 90 are equal to the product of a positive multiple of 5 and an odd number?
(A) 4
(B) 9
(C) 11
(D) 12
(E) 15
Rationale: The Question basically asks how many positive odd integers less than 90 are odd multiples of 5
So we have 5,15,25,35,45,55,65,75,85
= 9
Ans B
Answer: (B) 9
Question: If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many T digits does this integer consists of?
(A) 150
(B) 339
(C) 342
(D) 359
(E) 362
Rationale: Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer T= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C
Answer: (C) 342
Question: What is the smallest integer y for which 27^y> 3^24?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: 27^y> 3^24
Converting into the same bases:
27^y> 27^8
Therefore for the equation to hold true, y> 8 or y= 9
Option C
Answer: (C) 9
Question: A tradesman by means of his false balance defrauds to the extent of 50%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
(A) 120%
(B) 125%
(C) 150%
(D) 100%
(E) 115%
Rationale: g% = 50 + 50 + (50*50)/100
= 125%
ANSWER:B
Answer: (B) 125%
Question: The ratio of two natural numbers is 5:6. If a certain number is added to both the numbers, the ratio becomes 7:8. If the larger number exceeds the smaller number by 10, find the number added?
(A) 10
(B) 87
(C) 20
(D) 72
(E) 74
Rationale: Let the two numbers be 5x and 6x.
Let the number added to both so that their ratio becomes 7:8 be k.
(5x + k)/(6x + k) = 7/8
42x = 7k => k = 2x.
6x - 5x = 10 => x = 10
k = 2x = 20.
Answer:C
Answer: (C) 20
Question: Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is?
(A) 11
(B) 16
(C) 77
(D) 88
(E) 99
Rationale: Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4
Suppose Tanya takes x days to do the work.
5:4 :: 20:x => x= 16 days.
Hence, Tanya takes 16 days to complete the work.
Answer: B
Answer: (B) 16
Question: If the charge of staying in a student youth hostel $18.00/day for the first week, and $15.00/day for each additional week, How much does it cost to stay for 23 days?
(A) $336
(B) $289
(C) $282
(D) $274
(E) $286
Rationale: Total number of days of stay = 23
Charge of staying in first week = 18*7 = 126 $
Charge of staying for additional days =(23-7)*15 = 16*15 = 240 $
Total charge =126 +240 = 366$
Answer A
Answer: (A) $336
Question: A worker makes a toy in every 2h. If he works for 80h, then how many toys will he make ?
(A) 40
(B) 54
(C) 45
(D) 39
(E) None
Rationale: Answer
Let number of toys be N.
More hours, More toys (Direct proportion)
2 : 80 : : 1 : N
⇒ N = 80/2 = 40 toys
Correct Option: A
Answer: (A) 40
Question: In a school of 850 boys, 44% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) 120
(B) 125
(C) 153
(D) 200
(E) 250
Rationale: 44 + 28 + 10 = 82%
100 â€“ 82 = 18%
850 * 18/100 = 153
ANSWER A
Answer: (A) 120
Question: When a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: When a certain number X is divided by 61, the remainder is 24. What is the remainder when X is divided by 5?
Putting a value say x = 24 we get remainder as 24 when divided by 61.
When 24 divided by 5 we get 4 as remainder.
C is the answer.
Answer: (C) 4
Question: If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 11), what is the value of x?
(A) 9
(B) 11
(C) 13
(D) 15
(E) 17
Rationale: (2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 11)
2^x - 2^(x-2) = 3. 2^11
Hence x = 13.
Answer is C
Answer: (C) 13
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 2 2 1/8 kmph
(B) 2 3 1/2 kmph
(C) 4 2 1/2 kmph
(D) 2 2 1/2 kmph
(E) 2 2 4/2 kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 1/2 kmph
Answer:D
Answer: (D) 2 2 1/2 kmph
Question: Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount invested in scheme B?
(A) 6400
(B) 2777
(C) 2666
(D) 2888
(E) 1671
Rationale: Let the sum invested in scheme A be Rs. x and that in scheme B be Rs. (13900 - x). Then,
(x * 14 * 2)/100 + [(13900 - x) * 11 * 2]/100 = 3508
28x - 22x = 350800 - (13900 * 22)
6x = 45000 => x = 7500
So, sum invested in scheme B = (13900 - 7500) = Rs. 6400.
Answer: A
Answer: (A) 6400
Question: Three cannons are firing at a target. If their individual probabilities to hit the target are 0.9, 0.7, and 0.8 respectively, what is the probability that none of the cannons will hit the target after one round of fire?
prob. that all the cannons will hit the target = .06
prob. that none of the cannons will hit = 1 - .06 = .94
(A) 0.06
(B) 0.12
(C) 0.21
(D) 0.29
(E) 0.94
Rationale: The probability that eachdoesn'thit is: 0.1, 0.3, and 0.2. When we have multiple independent events, we multiply the probabilities:
.9*.7*.8 = 0.06.
Option: A
Answer: (A) 0.06
Question: A can finish a piece of work in 5 days. B can do it in 10 days. They work together for 1 day and then A goes away. In how many days will B finish the work?
(A) 8 days
(B) 5 days
(C) 6 days
(D) 7 days
(E) 9 days
Rationale: 1/5 + (1 + x)/10 = 1 => x = 7 days
Answer: D
Answer: (D) 7 days
Question: How many two letter words are formed using the letters of the word MICKY?
(A) 28
(B) 21
(C) 26
(D) 20
(E) 29
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 5P2
= 5 * 4 = 20.
Answer: D
Answer: (D) 20
Question: A three-person committee must be chosen from a group of 7 professors and 10 graduate students. If at least one of the people on the committee must be a professor, how many different groups of people could be chosen for the committee?
(A) 70
(B) 560
(C) 630
(D) 1,260
(E) 1,980
Rationale: Total number of ways to select at least one professor = Number of ways to select 3 people from 10 students and 7 professors - Number of ways to select 3 people from 10 student (i.e. without including any professor)
= 17C3 - 10C3 = 680 - 120 = 560
ANSWER:B
Answer: (B) 560
Question: The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 402 to 500 inclusive?
(A) 14,550
(B) 18,550
(C) 22,550
(D) 26,550
(E) 30,550
Rationale: 2 + 4 + 6 + 8 +...+ 100 = 2550
402 + 404 + ... + 500 = 50(400) + (2+4+...+100) = 20,000 + 2550 = 22,550
The answer is C.
Answer: (C) 22,550
Question: Number of students in institutes A and B were in the ratio of 7 : 15 respectively in 2012. In 2013, the number of students in institute A increased by 25% and number of students in institutes B increased by 26%, then what was the respective ratio between number of students in institutes A and B?
(A) 25 : 56
(B) 24 : 55
(C) 24 : 53
(D) 25 : 53
(E) 25 : 54
Rationale: Solution:
Ratio of students in 2012 in institutes A and B,
= 7 : 15.
Let number of students in institute A in 2012 = 700.
And Number of students in institutes B in 2012 = 1500.
25% increase in the number of students in 2013,
Now, number of students in Institute A,
= 700 + 25% of 700. = 875.
Number of students in B in 2013 as 26% students increased in B,
= 1500 + 26% of 1500 = 1890.
Current Ratio of the students,
= 875 /1890 = 25 : 54.
Answer: Option E
Answer: (E) 25 : 54
Question: A and B start a business, with A investing the total capital of Rs.5000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) A)2500
(B) B)3500
(C) C)5000
(D) D)6000
(E) E)8000
Rationale: Interest received by A from B = 10% of half of Rs.5000 = 10% * 2500 = 250.
Amount received by A per annum for being a working partner = 500 * 12 = Rs.1000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (250 + 1000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(250 + 1000 + P) = 2(P)
P = 1250
Total profit = 2P + 1000
= 2*1250+ 1000 = 3500
Answer:B
Answer: (B) B)3500
Question: In three annual examinations, of which the aggregate marks of each was 500, a student secured
average marks 45% and 55% in the first and the second yearly examinations respectively. To secure 60% average total marks, it is necessary for him in third yearly examination to secure marks :
(A) 300
(B) 350
(C) 400
(D) 450
(E) 500
Rationale: total marks:1500 for three exams
60% of 1500=900
first exam marks=45% of 500=225
second exam marks=55% of 500=275
let X be the third exam marks
225 + 275 + X =900
X=400
ANSWER:C
Answer: (C) 400
Question: If 1/a + 3/a + 4/a is an integer, which of the following must also be an integer?
(A) 12/a
(B) 3/a
(C) 8/a
(D) 9/a
(E) 15/a
Rationale: 1/a + 3/a + 4/a
=8/a
Answer C
Answer: (C) 8/a
Question: How long does a train 110 m long running at the speed of 36 km/hr takes to cross a bridge 132 m length?
(A) 82.1 sec
(B) 12.1 sec
(C) 24.2 sec
(D) 13.1 sec
(E) 12.15sec
Rationale: Speed = 36 * 5/18 = 10 m/sec
Total distance covered = 110 + 132 = 242 m.
Required time = 242/10 = 24.2 sec.
Answer:C
Answer: (C) 24.2 sec
Question: What is the greatest number of three digits which is divisible by 5, 10, 15 ?
(A) 985
(B) 970
(C) 955
(D) 990
(E) 999
Rationale: Greatest number of 3 digits = 999
LCM of 5, 10, 15 = 30
999 ÷ 30= 33, remainder = 9
Hence, greatest number of four digits which is divisible by 5,10,15
= 999 - 9 = 990
answer : D
Answer: (D) 990
Question: In a race with 30 runners where 6 trophies will be given to the top 6 runners (the trophies are distinct: first place, second place, etc), how many ways can this be done?
(A) 6^6 ways
(B) 8^9 ways
(C) 7^8 ways
(D) 8^7 ways
(E) 8^6 ways
Rationale: 6 people can be prized with distinct prizes in 6^6 ways
ANSWER:A
Answer: (A) 6^6 ways
Question: At what time between 6 and 7 are the hands of the clock coincide?
(A) 6:39
(B) 6:37
(C) 6:31
(D) 6:32
(E) 6:313
Rationale: For hour = 360/12 = 300300/hr
For Minute = full rotation = 36003600/hr
Let the line is 't' , for 6 = 6*30=18001800
then
30 t + 180=360 t
330t = 180
t = 180/330
t = 6/11 hr 6/11*60=360/11=32611611
Ans. D
Answer: (D) 6:32
Question: A fair coin with sides marked heads and tails is to be tossed eight times. What is the probability that the coin will land tails side up more than five times?
(A) 37/256
(B) 56/256
(C) 65/256
(D) 70/256
(E) 81/256
Rationale: More than 5 times tails = 6times +7times+8times = 8C6 + 8C7 + 8C8 = 37
- - - - - - - -
2 2 2 2 2 2 2 2
2^8 times total events and 37 events where tails side up .
So probability = 37/2^8 = 37/256 (Answer A)
Answer: (A) 37/256
Question: A certain bakery baked a batch of 450 cookies one day. Of those, 320 contained nuts, 230 contained chocolate chips, and 85 contained neither nuts nor chocolate chips. What is the fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch?
(A) 166
(B) 213
(C) 413
(D) 438
(E) 511
Rationale: Cookies which have both nuts and chocolate chips = 185
Let fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that
batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch = x
(185+x)/(450+x) = 6/10
=>1850 + 10x = 2700 + 6x
=> 4x = 850
=> x = 212.5
Therefore x = 213
Answer B
Answer: (B) 213
Question: The avg. age ofa group of 12 students is 20yers.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
(A) 22 years
(B) 23 years
(C) 24 years
(D) 25 years
(E) 26 years
Rationale: Total age of 12 students=12*20=240
If total age of 4 students=x
Then, (240+x)/(12+4) =(20+1), x=96
So average age of new students=96/4= 24 years
ANSWER:C
Answer: (C) 24 years
Question: A room has equal number of men and women. Eight women left the room, leaving twice as many men as women in the room . What was the total number of men and women present in the room initially?
(A) 28
(B) 30
(C) 31
(D) 32
(E) 27
Rationale: Assume that initial number of men = initial number of women = x
2(x-8) = x
=> 2x - 16 = x
=> x = 16
Total number of men and women = 2x = 2 × 16 = 32
Answer is D.
Answer: (D) 32
Question: In how many ways can you seat 4 people on a bench if one of them, Rohit, does not want to sit on the middle seat or at either end?
(A) 720
(B) 6
(C) 2880
(D) 5040
(E) 10080
Rationale: Since Rohit does not want to sit on the middle seat or at either end (3 chairs), then he can choose 1 chairs to sit. The remaining 3 people can sit in 3! ways. Thus the # of arrangements is 1*3! = 6.
Answer: B.
Answer: (B) 6
Question: The annual cost of owning and operating a car, C dollars, is a linear function of the distance, d kilometers, it is driven.
(A) 0.3d + 1609
(B) 0.3d + 16089
(C) 0.3d + 1600
(D) 0.3d + 1602
(E) 0.3d + 1601
Rationale: c = md + b
The cost is $ 4600 for 10 000 km
4600 = m (10 000) + b
10 000 m + b = 4600
b = -10 000 m + 4600 ------- (i)
The cost is $ 9100 for 25 000 km
9100 = m (25 000) + b
9100 = 25 000 m + b
25 000 m + b = 9100
b = -25 000 m + 9100 --------- (ii)
From equation (i) and (ii) we get;
-10 000 m + 4600 = -25 000 m + 9100
-10 000 m + 25 000 m = 9100 – 4600
15 000 m = 4500
m = 4500/15 000
m = 3/10
m = 0.3
Now, put the value of m = 0.3 in equation (i) we get;
b = -10 000 (0.3) + 4600
b = -3000 + 4600
b = 1600
Answer: m = 0.3 and b = 1600
(b) c = md + b
m = 0.3
b = 1600
c = 0.3d + 1600
Answer: C = 0.3d + 1600
Answer: (C) 0.3d + 1600
Question: Linda and Angela contract to paint a neighbor's house. Even though Linda spends 80% more time painting the house than Angela, each receives a payment of m dollars when the work is completed. If Angela decides to pay Linda n dollars so that they would have received the same compensation per hour worked, what is n in terms of m ?
(A) 1/2 m
(B) 1/3 m
(C) 1/4 m
(D) 1/5 m
(E) 1/6 m
Rationale: After the final transaction:
Angela received $(m-n) for t hours;
Linda received $(m+n) for 1.5t hours;
We are told that after that transaction they received the same compensation per hour: (m-n)/t=(m+n)/1.5t --> 1.5m-1.5n=m+n -->m=5n --> n=m/2.
Answer: A.
Answer: (A) 1/2 m
Question: The toll for crossing a certain bridge is $0.65 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $13.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker?
(A) 14
(B) 15
(C) 16
(D) 28
(E) 29
Rationale: Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.
If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: C
Answer: (C) 16
Question: How many 4-letter word with or without meaning can be formed out of the letters of the word 'LOGARITHMS' if repetition of letters is not allowed
(A) 5040
(B) 1254
(C) 4510
(D) 1203
(E) 4510
Rationale: 'LOGARITHMS' contains 10 different letters
Required number of words
= Number of arrangements of 100 letters taking
4 at a time
= 10P4
= 10 * 9 * 8 * 7
= 5040
Ans: A
Answer: (A) 5040
Question: If n is a 9-digit positive integer, all of whose digits are the same, which of the following must be true?
I. n is divisible by 3
II. n is divisible by 9
III. n is divisible by 10
(A) I and II only
(B) I only
(C) I and III only
(D) II and III only
(E) I, II and III
Rationale: Rule for divisibility by 3: The sum of the digits of the number should be multiple of 3
Rule for divisibility by 9: The sum of the nos digits of the number should be divisible by 9 or the number should be divisible by 3 two times.
Rules for divisibility by 9: The sum of the digits should a multiple of 9
Consider no 11111111...9 times = The sum 9*1=27----> divisbible by 3,9
consider number to be 222....9 times, then sum of the no. 9*2=18 divisible by 3,9
So why so because when you sum the numbers either you can add the digits 9 times or multiply the digit *9..
Note that since 9 is divisble by 9 and 3 and thus the sum of the nos will be divisible by all the nos.
A
Answer: (A) I and II only
Question: Bill made a profit of 10% by selling a product. If he had purchased that product for 10% less and sold it at a profit of 30%, he would have received $28 more. What was his original selling price?
(A) $200
(B) $260
(C) $320
(D) $380
(E) $440
Rationale: Let P be the original purchase price of the product.
Bill originally sold the product for 1.1*P.
In the second scenario, the purchase price is 0.9*P.
A 30% profit means the selling price would be 1.3*0.9*P = 1.17*P
Thus, according to the information in the question, 1.17P - 1.1P = 28
0.07 = 28
P = 400
The original selling price was 400*1.1 = 440.
The correct answer is E.
Answer: (E) $440
Question: In a diving competition, each diver has a 25% chance of a perfect dive. The first perfect dive of the competition, but no subsequent dives, will receive a perfect score. If Janet is the third diver to dive, what is her chance of receiving a perfect score? (Assume that each diver can perform only one dive per turn.)
(A) 1/5
(B) 1/15
(C) 4/25
(D) 9/64
(E) 61/125
Rationale: Probability = Favourable Outcomes / Total Outcomes = 1 - (Unfavourable Outcomes / Total Outcomes)
Given:Probability of Perfect dive = 0.25 = 25/100 = 1/4
i.e. Probability of Non-Perfect dive = 0.75 = 75/100 =3/4
The probability of Janet to dive and get a perfect score depends on that other other previous two dives must be Imperfect
Method-1:
i.e. Probability of First two being Imperfect and Third being Perfect dive = (3/4)*(3/4)*(1/4) =9/64
D
Answer: (D) 9/64
Question: If 40 men take 15 days to to complete a job, in how many days can 25 men finish that work?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 28
Rationale: Ans. 24 days
Answer: (A) 24
Question: Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
(A) 50 m
(B) 72 m
(C) 80 m
(D) 82 m
(E) 84 m
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
ANSWER:A
Answer: (A) 50 m
Question: The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is:
(A) 1 months
(B) 4 months
(C) 7 months
(D) 9 months
(E) 4 months
Rationale: S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time = 100 x 80	year	=	1	year = 4 months.
1600 x 15	3
View Answer Discuss in Forum Workspac
Answer:B
Answer: (B) 4 months
Question: The average weight of D, E and F is 42 kg. If the average weight of D and E be 35 kg and that of E and F be 41 kg, what is the weight of E?
(A) 23 Kg
(B) 24 Kg
(C) 25 Kg
(D) 26 Kg
(E) 27 Kg
Rationale: Let the weight of D, E and F are a,b and c respectively.
Average weight of D,E and F = 42
a + b + c = 42 × 3 = 126 --- equation(1)
Average weight of D and E = 35
a + b = 35 × 2 = 70 --- equation(2)
Average weight of E and F = 41
b + c = 41 × 2 = 82 --- equation(3)
equation(2) + equation(3) - equation(1)
=> a + b + b + c - (a + b + c) = 70+82 - 126
=> b = 152-126 = 26
Weight of B = 26 Kg
ANSWER:D
Answer: (D) 26 Kg
Question: A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?
(A) 48 min. past 19
(B) 48 min. past 12
(C) 48 min. past 10
(D) 48 min. past 11
(E) 48 min. past 14
Rationale: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
hrs of this clock = 24 hours of the correct clock.
29 hours of this clock = hrs of the correct clock
= 28 hrs 48 min of the correct clock.
Therefore, the correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.
Answer: A) 48 min. past 12.
Answer: (A) 48 min. past 19
Question: If the number 67925*4 is completely divisible by 8, then the smallest whole number in place of * will be?
(A) 1
(B) 2
(C) 0
(D) 4
(E) None of these
Rationale: The number 5x4 must be divisible by 8.
x=0 as 504 is divisible by 8.
Correct Option : C
Answer: (C) 0
Question: The first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 40%?
(A) 4
(B) 6
(C) 5
(D) 2
(E) 8
Rationale: We need on-time departure rate to be higher than 4/10, so it should be at least 5/11, which means that 5 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 5-3=2 subsequent flights need to depart on-time.
Answer: D
Answer: (D) 2
Question: Pam and Stanley packed several boxes with reams of paper. While both packed, Pam packed 40% of the boxes. After Pam stopped, Stanley packed the same number of boxes that he had packed while working with Pam. What is the ratio of the number of boxes Pam packed to the number of boxes Stanley packed?
(A) 1 to 4
(B) 1 to 3
(C) 2 to 6
(D) 3 to 4
(E) 3 to 2
Rationale: Correct Answer: C
Solution: C. We know that when Pam and Stanley were both working, the ratio was 2 boxes by Pam to 3 boxes by Stanley. We also know that Stanley continued working after Pam stopped. He packed as many boxes alone as he had packed whlie working with Pam, effectively doubling his number of boxes. Thus, the ratio of Pam's boxes to Stanley's boxes is 2 to 6. Answer C is correct.
Answer: (C) 2 to 6
Question: If 85 percent of the test takers taking an old paper and pencil GMAT exam answered the first question on a given math section correctly, and 65 percent of the test takers answered the second question correctly, and 5 percent of the test takers answered neither question correctly, what percent answered both correctly?
(A) 60 %
(B) 55 %
(C) 70%
(D) 75%
(E) 80%
Rationale: {Total} = {First correctly} + {Second correctly} - {Both correctly} + {Neither correctly}
100 = 85 + 65 - {Both correctly} + 5
{Both correctly} = 55.
Answer: B.
Answer: (B) 55 %
Question: If x and j are integers and 2x–j= 11, then 4x+ j CANNOT be
(A)  –5
(B)  1
(C)  13
(D)  17
(E)  551
Rationale: 2x-j=11....j=2x-11
4x+j=4x+2x-11=6x-11
6x-11=-5...x=1
6x-11=1... x=2
6x-11=13...x=4
6x-11=17..X is not integer
6x-11=551..X is not integer
I think the choice E is 55 not 551. Otherwise both DE CANNOT be solution=D
Answer: (D)  17