mathewhe/aqua_rat huggingface dataset:
Question: A completes a work in 10 days and B complete the same work in 15 days. If both of them work together, then the number of days required to complete the work will be
(A) 6 days
(B) 9 days
(C) 10 days
(D) 12 days
(E) 13 days
Rationale: If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days
Therefore, here, the required number of days = 10 × 15/ 25= 6 days.
Answer : A
Answer: (A) 6 days
Question: A train 125 m long passes a man, running at 4 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
(A) 28
(B) 49
(C) 88
(D) 22
(E) 12
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 4) km/hr. x - 4 = 45 ==> x
= 49 km/hr.Answer:B
Answer: (B) 49
Question: Four people each roll a four die once. Find the probability that at least two people will roll the same number ?
(A) 13/18
(B) 13/17
(C) 13/11
(D) 13/19
(E) 13/12
Rationale: The number of ways of rolling a dice where no two numbers probability that no one rolls the same number = 6 x 5 x 4 x 3
Now total possibilities of rolling a dice = 6464
The probability that a no one gets the same number = 6×5×4×364=5186×5×4×364=518
So the probability that at least two people gets same number = 1−5/18=13/18
Answer:A
Answer: (A) 13/18
Question: In a consumer survey, 80% of those surveyed liked at least one of three products: 1, 2, and 3. 50% of those asked liked product 1, 30% liked product 2, and 20% liked product 3. If 5% of the people in the survey liked all three of the products, what percentage of the survey participants liked more than one of the three products?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: pick 100 and x= all set with exactly two items
80=30+50+20 -(X)-10
X=10
so the answer is 10+5/100= 15%
answer C
Answer: (C) 15
Question: A farmer has an apple orchard consisting of Fuji and Gala apple trees. Due to high winds this year 10% of his trees cross pollinated. The number of his trees that are pure Fuji plus the cross-pollinated ones totals 153, while 3/4 of all his trees are pure Fuji. How many of his trees are pure Gala?
(A) 27
(B) 33
(C) 55
(D) 77
(E) 88
Rationale: Let f = pure fuji , g = pure gala and c - cross pollinated.
c = 10% of x where x is total trees.
c = .1x
also 3x/4 = f and c+f = 153 => .1x + 3/4x = 153 => x = 180
180 - 153 = pure gala = 27.
Answer A
Answer: (A) 27
Question: If the operation Ø is defined for all positive integers x and w by x Ø w = (2^x)/(2^w) then (3 Ø 1) Ø 1 = ?
(A) 2
(B) 4
(C) 8
(D) 16
(E) 32
Rationale: 3 Ø 1 = 2^3/2^1 = 4
4 Ø 1 = 2^4/2 = 8
The answer is C.
Answer: (C) 8
Question: A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 8% of bananas were rotten. Find the percentage of fruits in good condition.
(A) 87.8%
(B) 87.9%
(C) 37.8%
(D) 87.7%
(E) 22.8%
Rationale: otal number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 × 600
= 9000/100
= 90
Number of rotten bananas = 8% of 400
= 8/100 × 400
= 3200/100
= 32
Therefore, total number of rotten fruits = 90 + 32 = 122
Therefore Number of fruits in good condition = 1000 - 122 = 878
Therefore Percentage of fruits in good condition = (878/1000 × 100)%
= (87800/1000)%
= 87.8%
Answer:A
Answer: (A) 87.8%
Question: A can run 1 km in 3 min. 10 sec. and B can cover the same distance in 3 min. 20 sec. By what distance can A beat B ?
(A) 50 m
(B) 18 m
(C) 96 m
(D) 23 m
(E) 13 m
Rationale: Soln:Clearly, A beats B by 10 sec.
Distance covered by B in 10 sec. = (1000 x 10 )/200m = 50 m.
Therefore A beats B by 50 metres.
Option A
Answer: (A) 50 m
Question: Michael earns $7.00 per hour for the first 40 hours he works per week, and twice this rate for overtime. If Michael earned $320 last week, how many hours did he work?
(A) 43
(B) 44
(C) 45
(D) 46
(E) 47
Rationale: $7*40 + $12*x = $320 --> x = 3 hours.
Total working hours = 40 + 3 = 43.
Answer: A.
Answer: (A) 43
Question: At a certain high school, a student’s popularity is determined by his or her locker number. Whoever has the locker number with the greatest number of distinct prime factors is the most popular student in the school. If Johanna, Jamal, Brianna, and Dyson get lockers with the numbers 300, 400, 150, and 420, respectively, who is the most popular student?
(A) Johanna
(B) Jamal
(C) Brianna
(D) Dyson
(E) They have equal popularity
Rationale: Distinct prime factors of 300 (Johanna) : 3, 2 5
Distinct prime factors of 400 (Jamal): 2 and 5.
Distinct prime factors of 150 (Brianna): 2,3, and 5
Distinct prime factors of 420 (Dyson): 2,3,5 and 7.
So most popular student - Dyson
Answer D
Answer: (D) Dyson
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. Find the distance light travels in 100 years?
(A) 587 × 108 miles
(B) 587 × 10-12 miles
(C) 587 × 1010 miles
(D) 587 × 10-10 miles
(E) 587 × 1012 miles
Rationale: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
Answer is B.
Answer: (B) 587 × 10-12 miles
Question: If an object travels at ten feet per second, how many feet does it travel in one hour?
(A) 30
(B) 300
(C) 720
(D) 1800
(E) 36000
Rationale: Speed = 10 feet per second.
1 Hour= 60X60 Seconds = 3600 Seconds.
Total no of feet traveled in 1 hour = 3600X10 = 36000
Answer E
Answer: (E) 36000
Question: Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent?
(A) 20%
(B) 80%
(C) 100%
(D) 180%
(E) 200%
Rationale: Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
[(2 - 1)/1] * 100% = 100%
ANSWER:C
Answer: (C) 100%
Question: What is the rate percent when the simple interest on Rs.900 amount to Rs.160 in 4 Years?
(A) 5%
(B) 7%
(C) 9%
(D) 4.4%
(E) 4%
Rationale: 160 = (900*4*R)/100
R = 4.4%
Answer: D
Answer: (D) 4.4%
Question: A school having four classes only have student strength of 10, 50, 30 and 10 respectively. The pass percentages of these classes are 20%, 30%, 60% and 100% respectively. What is the pass percentage for the entire school?
(A) 56%
(B) 76%
(C) 34%
(D) 66%
(E) 45%
Rationale: 20% of 10+30% of 50+60% of 30+100% of 10
=2+15+18+10 =
now 45 of 100
= 45%
ANSWER:E
Answer: (E) 45%
Question: The simple form of the ratio 2/3:2/5 is
(A) 5:7
(B) 5:2
(C) 5:9
(D) 5:3
(E) 5:4
Rationale: 2/3 : 2/5 = 10:6 = 5:3
Answer: D
Answer: (D) 5:3
Question: In a group of 68 students, each student is registered for at least one of three classes – History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-nine students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
(A) 13
(B) 10
(C) 15
(D) 8
(E) 7
Rationale: A U B U C = A + B + C - AB-BC-AC + ABC
68 = 25 + 25+ 39 -AB-BC-AC +3 => AB+BC+AC = 24
Exactly Two classes = AB+BC+AC - 3ABC = 24 -3*3 = 15
Hence C
Answer: (C) 15
Question: What is the place value of 7 in the numeral 2734?
(A) 450
(B) 460
(C) 480
(D) 500
(E) 700
Rationale: Option 'E'
7 * 100 = 700
Answer: (E) 700
Question: SI on a certain sum of money for 3 yrs at 8 percent /annum is 1/2 the CI on Rs.4000 for 2 yrs at 10 percent/ annum. The sum placed on SI is?
(A) Rs. 1650
(B) Rs. 1700
(C) Rs. 1750
(D) Rs. 1950
(E) Rs. 1980
Rationale: C.I.
= Rs. 4000 x 1 + 10 2 - 4000
100
= Rs. 4000 x 11 x 11 - 4000
10 10
= Rs. 840.
Sum = Rs. 420 x 100 = Rs. 1750.
3 x 8
C
Answer: (C) Rs. 1750
Question: A retailer bought a hat at wholesale and marked it up 70% to its initial price of $34. By how many more dollars does he need to increase the price to achieve a 100% markup?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Let x be the wholesale price.
Then 1.7x= 34 and x = 34/1.7 = 20.
To achieve a 100% markup, the price needs to be $40.
The retailer needs to increase the price by $6 more.
The answer is C.
Answer: (C) 6
Question: There are 6 books on a shelf, of which 2 are paperbacks and 4 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?
(A) a) 40
(B) b) 14
(C) c) 50
(D) d) 55
(E) e) 60
Rationale: approach 1
at-least 1 paper back = total - no paper back
6c4-4c4 = 14
approach 2
at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back
= 2c1*4c3+2c2*4c2 = 14
Answer is B
Answer: (B) b) 14
Question: If you are given $2, and the amount doubles every day, how much money will you have after 12 days?
(A) $256
(B) $512
(C) $1024
(D) $2048
(E) $4096
Rationale: 2^12=4096
The answer is E.
Answer: (E) $4096
Question: Average of five numbers is -10, and the sum of three of the numbers is 16, wat is the average of the other 2 numbers?
(A) -33
(B) 33
(C) 32
(D) -31
(E) 24
Rationale: Let the five numbers be a, b, c, d, e. Then their average is (a+b+c+d+e5)=10.(a+b+c+d+e5)=10.
Now three of the numbers have a sum of 16, say, a+b+c=16a+b+c=16.
So substitute 16 for a+b+ca+b+c in the average above: (16+d+e5)=10.(16+d+e5)=10.
Solving this equation for d+ed+e gives d+e=−66d+e=−66.
Finally, dividing by 2 (to form the average) gives (d+e2)=−33.(d+e2)=−33.
Hence, the answer is A: -33
Answer: (A) -33
Question: In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:
(A) 5 km/hr
(B) 15 km/hr
(C) 50 km/hr
(D) 20 km/hr
(E) 25 km/hr
Rationale: Let Abhay's speed be x km/hr.
Then,(30/x - 30/2x)= 3
6x = 30
x = 5 km/hr.
ANSWER A
Answer: (A) 5 km/hr
Question: The wages earned by Robin is 30% more than that earned by Erica. The wages earned by Charles is 60% more than that earned by Erica. How much % is the wages earned by Charles more than that earned by Robin?
(A) 23%
(B) 18.75%
(C) 30%
(D) 50%
(E) 100%
Rationale: Explanatory Answer
Let the wages earned by Erica be $100
Then, wages earned by Robin and Charles will be $130 and $160 respectively.
Charles earns $30 more than Robin who earns $130.
Therefore, Charles' wage is 30/130*100 = 23.07%.
correct choice is (A)
Answer: (A) 23%
Question: In a certain lottery, the probability that a number between 1 and 15, inclusive, is drawn is 1/3 . If the probability that a number 1 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 15 is drawn?
(A) 2 by 3
(B) 1/3
(C) 1/4
(D) 1/6
(E) 2/5
Rationale: You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 1 or larger
Set 2: Number 15 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either12 or moreOR20 or less OR both)
2/3 + P(Set 2) - 1/3 = 1
P(Set 2) = 2/3
Answer A
Answer: (A) 2 by 3
Question: When positive integer x is divided by 8, the quotient is y and the remainder is 2. When 2x is divided by 7, the quotient is 2y and the remainder is 4. What is the value of 6y – x?
(A) -1
(B) 1
(C) -2
(D) 2
(E) -3
Rationale: (1) x = 8y+2
(2) 2x = 14y+4
(2)-(1): x=6y+2
6y-x=-2
The answer is C.
Answer: (C) -2
Question: If the range of the set of numbers {140, 90, 135, 110, 170, 145, x, 100, 140} is 100, which of the following could be x?
(A) 170
(B) 190
(C) 210
(D) 230
(E) 250
Rationale: The range of the other 8 numbers is 170-90 = 80, so x must be either the smallest number or the largest number in the set.
Then x = 170-100 = 70 or x = 90+100 = 190
The answer is B.
Answer: (B) 190
Question: Sum of two numbers is 50. Two times of the difference of first and seceond is 20. Then the numbers will be?
(A) 10, 40
(B) 20, 30
(C) 35, 15
(D) 30, 20
(E) 15, 35
Rationale: Explanation:
x + y = 50
2x Ã¢â‚¬â€œ 2y = 20
x = 30 y = 20
Answer: D
Answer: (D) 30, 20
Question: B, C and D invested Rs.6400, Rs.1600 and Rs.2400 respectively, in a partnership business. Find the share of D in profit of Rs.26000 after a year?
(A) 6400
(B) 6300
(C) 6100
(D) 6000
(E) 6200
Rationale: Explanation:
6400:1600:2400
8:2:3
3/13 * 26000 = 6000
D)
Answer: (D) 6000
Question: A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are?
(A) Rs.10,500, Rs. 13,500, Rs. 16,500
(B) Rs.10,500, Rs. 13,500, Rs. 16,580
(C) Rs.10,500, Rs. 13,500, Rs. 16,560
(D) Rs.10,500, Rs. 13,500, Rs. 16,509
(E) Rs.10,500, Rs. 13,503, Rs. 16,501
Rationale: A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
Answer: A
Answer: (A) Rs.10,500, Rs. 13,500, Rs. 16,500
Question: Two persons A and B take a field on rent. A puts on it 21 horses for 3 months and 15 cows for 2 months; B puts 15 cows for 6months and 40 sheep for 7 1/2 months. If one day, 3 horses eat as much as 5 cows and 6 cows as much as 10 sheep, what part of the rent should A pay?
(A) 1/3
(B) 1/6
(C) 1/8
(D) 1/7
(E) 1/1
Rationale: 3h = 5c
6c = 10s
A = 21h*3 + 15c*2
= 63h + 30c
= 105c + 30c = 135c
B = 15c*6 + 40s*7 1/2
= 90c + 300s
= 90c + 180c = 270c
A:B = 135:270
27:52
A = 27/79 = 1/3
Answer: A
Answer: (A) 1/3
Question: Jerry had an average score of 85 on his first eight quizzes. He had an
average score of 81 on his first nine quizzes. What score did he receive on
his ninth quiz?
(A) 49
(B) 51
(C) 53
(D) 55
(E) 57
Rationale: The sum of Jerry’s first 8 scores is 8 · 85 and the sum of his first 9 scores is 9 · 81, so he received
9 · 81 − 8 · 85 on his 9th quiz. You can do the arithmetic or note that the answer ends in a 9.
correct answer A
Answer: (A) 49
Question: E is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of E, and y is the minimum value of the sum of k distinct members of E, what is x + y?
(A)  kn
(B)  kn + k^2
(C)  kn + 2k^2
(D)  2kn – k^2
(E)  2kn
Rationale: Probably the easiest way to solve this question would be to assume some values for n and k.
Say n=3, so E, the set of the first n positive odd numbers would be: E={1, 3, 5};
Say k=1, so E, the maximum value of the sum of K distinct members of Z would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of E would simply be 1.
X+Y=5+1=6.
Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.
Answer: E.
Answer: (E)  2kn
Question: Johnny bought six peanut butter cans at an average price (arithmetic mean) of 36.5¢. If Johnny returned two cans to the retailer, and the average price of the remaining cans was 30¢, then what is the average price, in cents, of the two returned peanut butter cans?
(A) 5.5
(B) 11
(C) 47.5
(D) 66
(E) 49.5
Rationale: Total price of six cans = 6*36.5 = 219
Total price of 4 cans = 4*30 = 120
Total rice of two cans = 219 - 120 = 99
Average price of two cans = 99/2 = 49.5 c
Another way to do it is this:
Assume that the four leftover cans were of 30c each. The avg was 36.5c initially because the two cans were 36.5c each and were providing another 6.5c of cost to other 4 cans.
So cost of the two cans = 2*36.5 + 4*6.5 = 99
Avg cost of the two cans = 99/2 = 49.5c
Answer (E)
Answer: (E) 49.5
Question: What is difference between biggest and smallest fraction among 2/5, 3/4, 4/5 and 5/6
(A) 2/5
(B) 3/5
(C) 1/6
(D) 1/7
(E) None of these
Rationale: Explanation:
2/5 = .4, 3/4 = .75, 4/5 = .8 and 5/6 = .833
So biggest is 5/6 and smallest is 2/5
Their difference is 5/6 - 2/5 = 13/30
Option E
Answer: (E) None of these
Question: In how many ways can 5 boys be allotted four different sofas such that none of the sofas are empty and all the 5 boys are accommodated?
(A) 300
(B) 290
(C) 280
(D) 260
(E) 240
Rationale: 4 boys can be selected from 5 boys in 5C4 ways = 5
4 boys can be arranged in 4 rooms in 4! ways
and since 1 boy has to share a room with one of the 4 boys, therefore total ways = 2! = 2
Hence total number of ways in which allocation can be done = 5C4 * 4! * 2! = 5*2*4! =240
E
Answer: (E) 240
Question: There are 9 books on a shelf that consist of 2 paperback books and 7 hardback books. If 5 books are selected at random without replacement, how many different combinations are there which include at least one paperback book?
(A) 85
(B) 95
(C) 105
(D) 115
(E) 125
Rationale: The total number of ways to select 5 books is 9C5 = 126
The number of ways which do not include any paperbacks is 7C5 = 21
The number of combinations with at least one paperback is 126-21 = 105
The answer is C.
Answer: (C) 105
Question: Power saving (in %) of a bulb is directly proportional to square root of its efficiency. By how much % is power saving of bulb-1(efficiency 0.8) greater than power saving of bulb-2 (efficiency 0.2)?
(A) 60%
(B) 70%
(C) 80%
(D) 90%
(E) 100%
Rationale: Power, P1=k∗sqrt(0.8)
Power, P2=k∗sqrt(0.2)
Difference = P1−P2=k∗sqrt(0.8)−k∗sqrt(0.2)
% greater =k∗sqrt(0.8)−k∗sqrt(0.2)/k∗sqrt(0.2)∗100
= 100%.
Hence, E
Answer: (E) 100%
Question: The speed at which a man can row a boat in still water is 18 kmph. If he rows downstream, where the speed of current is 6 kmph, what time will he take to cover 100 metres?
(A) 6.67seconds
(B) 18 seconds
(C) 26 seconds
(D) 14.99 seconds
(E) 6 seconds
Rationale: Speed of the boat downstream = 18 +6
= 24 kmph
= 24 * 5/18 = 6.67m/s
Hence time taken to cover 100 m = 100/6.67
= 14.99 seconds.
Answer:D
Answer: (D) 14.99 seconds
Question: By selling 14 pencils for a rupee a man loses 22%. How many for a rupee should he sell in order to gain 22%?
(A) 10
(B) 9
(C) 7
(D) 6
(E) 4
Rationale: 88% --- 14
122% --- ?
88/122 * 14 = 10
Answer: A
Answer: (A) 10
Question: A tank holds x gallons of a saltwater solution that is 20% salt by volume. One Fourth of the water is evaporated, leaving all of the salt. When 8 Gallons of water and 16 gallons of salt are added, the resulting mixture is 33 1/3 % salt by volume. What is the value of x?
(A) 120
(B) 75
(C) 100
(D) 150
(E) 175
Rationale: Nope, 150. I can only get it by following PR's backsolving explanation. I hate that.
Original mixture has 20% salt and 80% water.
Total = x
Out of which Salt = 0.2x and water = 0.8x
Now, 1/4 water evaporates and all salt remains.
So what remains is 0.2x salt and 0.6x water.
Now 16 gallons salt is added and 8 gallons of water is added.
So salt now becomes -> (0.2x + 16) and water --> (0.6x+8)
Amount of salt is 33.33% of total. So amount of water is 66.66%. So salt is half of the volume of water.
So (0.2x+16) = (0.6x+8)/2 => 0.2x= 24
Solving, x = 120
Answer : A
Answer: (A) 120
Question: The distance between towns A and B is 300 km. One train departs from town A and another train departs from town B, both leaving at the same moment of time and heading towards each other. We know that one of them is 10 km/hr faster than the other. Find the speeds of both trains if 2 hours after their departure the distance between them is 40 km.
(A) 22
(B) 27
(C) 236
(D) 90
(E) 81
Rationale: Let the speed of the slower train be xx km/hr. Then the speed of the faster train is (x+10)(x+10) km/hr. In 2 hours they cover 2x2x km and 2(x+10)2(x+10)km, respectively. Therefore if they didn't meet yet, the whole distance from A to B is 2x+2(x+10)+40=4x+602x+2(x+10)+40=4x+60 km. However, if they already met and continued to move, the distance would be 2x+2(x+10)−40=4x−202x+2(x+10)−40=4x−20km. So we get the following equations:
4x+60=3004x+60=300
4x=2404x=240
x=60x=60 or
4x−20=3004x−20=300
4x=3204x=320
x=80x=80
Hence the speed of the slower train is 60 km/hr or 80 km/hr and the speed of the faster train is 70 km/hr or 90 km/hr.
Answer:D
Answer: (D) 90
Question: In Rwanda, the chance for rain on any given day is 1/2. What is the probability that it rains on 4 out of 6 consecutive days in Rwanda?
(A) 4/7
(B) 3/7
(C) 15/64
(D) 4/28
(E) 28/135
Rationale: using Binomial. theorem
nCr (p)^r (q)^n-r
6C4 (1/2)^4 (1/2)^r
which is 15/64
Answer is C.
Answer: (C) 15/64
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 72 km/hr. What is the length of the platform?
(A) 240
(B) 188
(C) 177
(D) 260
(E) 320
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Length of the train = 20 * 20 = 400 m.
Let the length of the platform be x m . Then,
(x + 400)/36 = 20 => x = 320.
Answer: E
Answer: (E) 320
Question: Divide $500 among Y,Z in the ratio 2:8. How many $ that Z get?
(A) $100
(B) $200
(C) $300
(D) $500
(E) $400
Rationale: Sum of ratio terms = 2+8 = 10
Z = 500*8/10 = $400
Answer is E
Answer: (E) $400
Question: A certain bag of gemstones is composed of two-thirds diamonds and one-third rubies. If the probability of randomly selecting two diamonds from the bag, without replacement, is 5/12, what is the probability of selecting two rubies from the bag, without replacement?
(A) 5/36
(B) 5/24
(C) 1/12
(D) 1/6
(E) 1/4
Rationale: 2/3 * (2X-1) / (3X-1) = 5/ 12 => X = 3
So total gems = 9
and probability of ruby = 1/3 * 2/8 = 1/12
answer 1/12 C
Answer: (C) 1/12
Question: A set of numbers has the property that for any number t in the set, t - 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. -5
II. 11
III. 6
(A)  I only
(B)  II only
(C)  I and II only
(D)  II and III only
(E)  I, II, and III
Rationale: The question is which of the followingmustbe in the set, notcouldbe in the set.
If -1 is in the set so must be -1-2=-3, as -3 is in the set so must be -3-2=-5, as -5 is in the set so must be -5-2=5 and so on. So basically knowing that -1 is in the set we can say that ALL odd numbers less than -1 are also in the set.
Answer: A.
Answer: (A)  I only
Question: At exactly what time past 9:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time?
(A) 20 13/21 minutes past 7:00
(B) 20 13/17 minutes past 7:00
(C) 21 3/23 minutes past 7:00
(D) 21 9/11 minutes past 9:00
(E) 22 4/9 minutes past 7:00
Rationale: 5.5 is the angle between minute n hour, this is what I was taught...so shouldn't it be solve by dividing 90 with 5.5?
That would have been the case if your initial difference between the hour and the minute hand was = 0 degrees or in other words, both minute and hour hands were at the same location. But as per the question, you are asked for time AFTER 9:00. At 9:00, the angle between the hour and the minute hand is 210 degrees. you need to take this into account as well.
So in order for the difference to decrease to 90 degrees, the minute hand must eat away this difference of 210-90 = 120 degree at the rate of 5.5 degrees per minute ---> 120/5.5 = 21 9/11 minutes.
Thus, D is the correct answer.
Answer: (D) 21 9/11 minutes past 9:00
Question: Three numbers are in the ratio 3:5:7. The largest number value is 63. Find difference between Smallest & largest number is?
(A) 20
(B) 24
(C) 30
(D) 34
(E) 36
Rationale: == 3:5:7
Total parts = 15
= The largest number value is 63
= The largest number is = 7
= Then 7 parts -----> 63 ( 7 * 9 = 63 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 36 (4 * 9 = 36)
E
Answer: (E) 36
Question: Working alone, printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 16, 10, and 20 hours, respectively. What is the ratio of the time it takes printer X to do the job, working alone at its rate, to the time it takes printers Y and Z to do the job, working together at their individual rates?
(A) 7/4
(B) 10/3
(C) 12/5
(D) 15/7
(E) 18/11
Rationale: The time it takes printer X is 16 hours.
The combined rate of Y and Z is 1/10 + 1/20 = 3/20
The time it takes Y and Z is 20/3
The ratio of times is 16 / (20/3) = 3*16/20 = 12/5
The answer is C.
Answer: (C) 12/5