mathewhe/aqua_rat huggingface dataset:
Question: Calculate the number of bricks, each measuring 25 cm x 15 cm x 8 cm required to construct a wall of dimensions 10 m x 4 cm x 6 m when 10% of its volume is occupied by mortar ?
(A) 720
(B) 600
(C) 660
(D) 6000
(E) 650
Rationale: Explanation:
Let the number of bricks be 'N'
10 x 4/100 x 6 x 90/100 = 25/100 x 15/100 x 8/100 x N
10 x 4 x 6 x 90 = 15 x 2 x N => N = 720.
ANSWER IS A
Answer: (A) 720
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in five hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
(A) 65 minutes
(B) 66 min
(C) 56 minutes
(D) 69 minutes
(E) 46 minutes
Rationale: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 5 hours.
His speed = 180/5 = 36 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 36 + 10 = 46km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 3.9 hours respectively. Hence difference in the time taken = 1.1 hours = 66 minutes.
ANSWER:B
Answer: (B) 66 min
Question: Two machines, Y and Z, work at constant rates producing identical items. Machine Y produces 5 items in the same time Machine Z produces 2 items. If machine Y takes 9 minutes to produce a batch of items, how many minutes does it take for machine Z to produce the same number of items?
(A) 6
(B) 9
(C) 9 1/2
(D) 22.5
(E) 13 1/2
Rationale: rate z/rate y=2/5
time z/time y=5/2
5/2*9=22.5 minutes
D
Answer: (D) 22.5
Question: A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%?
(A) 221
(B) 144
(C) 666
(D) 888
(E) 212
Rationale: Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144
Answer:B
Answer: (B) 144
Question: If the cost price of 22 articles is equal to the selling price of 16 articles, What is the percentage of profit or loss that the merchant makes?
(A) 20% loss
(B) 37.5 % profit
(C) 37.5 % loss
(D) 30.33% loss
(E) None of these
Rationale: Explanation :
Let Cost price of 1 article be Re.1.
Therefore, Cost price of 22 articles = Rs. 22.
Selling price of 16 articles = Rs. 22
Therefore, Selling price of 22 articles is :-
=>22/16Ã—22
=>30.25.
Therefore, Profit = Selling price - Cost price.
=>30.25âˆ’22=8.25
Hence, the percentage of profit = profit x 100/C.P.
=>8.25/22Ã—100.
=>37.5% Profit.
Answer : B
Answer: (B) 37.5 % profit
Question: The price of 5 kilograms of premium fertilizer is the same as the price of 10 kilograms of regular fertilizer. If the price of premium fertilizer is y cents per kilogram more than the price of regular fertilizer, what is the price, in cents, per kilogram of premium fertilizer?
(A) y/30
(B) 5/6*y
(C) 6/5*y
(D) 2y
(E) 6y
Rationale: Usingpfor premium andrfor regular, I got two equations from the question stem:
5p = 10r and p = r+y
Substitute for p: 5(r+y) = 10r
Distribute: 5r + 5y = 10r
Subtract 5r from both sides: 5y = 5r
Plug back into the first equation: 5p = 10(y)
Distribute: 5p = 10y
Divide both sides by 5: p = 2y
The answer is D.
Answer: (D) 2y
Question: Given that p is a positive even integer with a positive units digit, if the units digit of p^3 minus the units digit of p^2 is equal to 0, what is the units digit of p - 3?
(A) 10
(B) 8
(C) 7
(D) 3
(E) 11
Rationale: p is a positive even integer with a positive units digit--> the units digit of p can be 2, 4, 6, or 8 -->
In order the units digit of p^3 - p^2 to be 0, the units digit of p^3 and p^2 must be the same. Thus the units digit of p can be 0, 1, 5 or 6.
Intersection of values is 6, thus the units digit of p - 3 is 6 - 3 = 3.
Answer: D.
Answer: (D) 3
Question: A taxicab fare costs x dollars for the first quarter of a mile and 1/4*x dollars for each quarter of a mile after that. How much will the total cost be for a 3/2 mile ride?
(A) 3x
(B) 13/4*x
(C) 10x
(D) 5/4*x
(E) 2.5x
Rationale: 3/2 miles = 1+1/2 miles
1+1/2 miles have 6 1/4 miles
1st 1/4 mile will cost= x
Remaining 5 1/4 miles will cost= 5/4 x
Total cost = x + 5/4 x= 9/4 x
ANSWER:B
Answer: (B) 13/4*x
Question: Find the odd man out. 10,30,50,72,95
(A) 10
(B) 30
(C) 50
(D) 72
(E) 95
Rationale: All except 72 are multiples of 5
Answer is D
Answer: (D) 72
Question: The sub-duplicate ratio of 25:49 is
(A) 4:3
(B) 5:7
(C) 6:4
(D) 1:4
(E) 2:3
Rationale: root(25):root(49)=5:7
ANSWER:B
Answer: (B) 5:7
Question: If in a $120 mln portfolio of stock, twice as much is invested in stock A as is invested in all the other stocks, how much is invested in all the other stocks?
(A) 40mln
(B) 50mln
(C) 60mln
(D) 70mln
(E) 80mln
Rationale: Let x denote the amount invested in all the other stocks. Then the amount invested in stock A is 2x. As we have the $120 mln portfolio, x+2x=3x=120 mln from where x=40 mln.
Answer: A
Answer: (A) 40mln
Question: The cost price of 13 articles is equal to the selling price of 11 articles. Find the profit percent?
(A) 67 2/16%
(B) 45 2/17%
(C) 18 2/11%
(D) 23 2/13%
(E) 14 2/10%
Rationale: C
13 CP = 11 SP
11 --- 2 CP
100 --- ? =>18 2/11%
Answer: (C) 18 2/11%
Question: From the word 'INTENSIFICATION', how many independent words can be made with-out changing the order of the letters and using each letter only once ?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 9
Rationale: Explanation:
The words formed are
IN, TEN, INTENS and CATION
Answer: B) 4
Answer: (B) 4
Question: If the city centers of New York and London are 3,471 miles apart, which of the following is closest to the distance between the city centers in inches? (There are 5,280 feet in a mile.)
(A) 1.75 × 10^7
(B) 1.83 × 10^7
(C) 2.10 × 10^8
(D) 2.10 × 10^9
(E) 2.20 × 10^10
Rationale: Distance in Miles = 3471
Given 1 mile = 5280 ft
So 3471 miles = 3471 X 5280 feet ~ 3500 x 5300 = 1.855 x 10^7 feet
1 feet is 12 inches, so the answer : 1.855 x 12 x 10^7 ~ 2.2 x 10^8.
Answer C
Answer: (C) 2.10 × 10^8
Question: List I: 3, 6, 10, 19
List II: x, 3, 10, 8, 19
(A)  6
(B)  7
(C)  8
(D)  9
(E)  10
Rationale: We start by calculating the median of the numbers of list I: 3, 6, 10, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers.
median = (6 + 10)/2
median = 16/2
median = 8
The median of list I is 7.
Looking at list II: x, 3, 6, 10, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 8 and therefore x is 8.
The answer is C.
Answer: (C)  8
Question: Every minute, G an type 55 words while H can type 70 in the same amount of time. IF they have 20 minutes to complete a 500 word document, how much time remains when they have finished typing the document? Answer in fractions.
(A) 290/77
(B) 1250/77
(C) 500/77
(D) 154/77
(E) 3750/77
Rationale: MInutes it takes for G to type 1 word: 1/55
Minutes it takes for H to type 1 word: 1/70
Minutes it takes for G and H to type 1 word: 1/55+1/70=5/154
Minutes it takes for G and H to type 500 words: 500x(5/154)=1250/77
MInutes remaining: 20-1250/77=290/77
Answer is A
Answer: (A) 290/77
Question: At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.20000?
(A) 6620
(B) 1879
(C) 2779
(D) 2672
(E) 2782
Rationale: A = 20000(11/10)3
= 26620
= 20000
----------
6620
Answer: A
Answer: (A) 6620
Question: Simplify: 2005-2000+10
(A) 1805
(B) 4509
(C) 2601
(D) 4508
(E) None of them
Rationale: 2005-2000+10
=2005-(2000/10)
=2005-200
=1805.
Answer is A
Answer: (A) 1805
Question: Find the Greatest Number that will devide 43, 91 and 183 so as to leave the same remainder in each case
(A) 4
(B) 7
(C) 9
(D) 13
(E) 15
Rationale: Explanation:
Required Number = H.C.F of (91- 43), (183- 91) and (183-43)
= H.C.F of 48, 92, and 140 = 4. Answer: A
Answer: (A) 4
Question: I. a^2 + 11a + 30 = 0,
II. b^2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?
(A) If a < b
(B) If a ≤ b
(C) If a > b
(D) If the relationship between a and b cannot be established
(E) If a ≥ b
Rationale: Explanation:
I. (a + 6)(a + 5) = 0
=> a = -6, -5
II. (b + 5)(b + 1) = 0
=> b = -5, -1 => a ≤ b
Option B
Answer: (B) If a ≤ b
Question: For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 902, what is the maximum possible sum of the length of x and the length of y?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: we know that : x > 1, y > 1, and x + 3y < 902,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 =1024 (it exceeds 1000, so, x can't be 2^10)
so, max value that X can take is 2^9 , for which has length of integer is 9.
now, since x =512 ,x+3y<902
so, 3y<390
==> y<130
so, y can take any value which is less than 130. and to get the maximum no of factors of smallest integer, we can say y=2^7
for 2^7 has length of integer is 7.
SO, combined together : 9+7 = 16.
E
Answer: (E) 16
Question: Population of a city in 20004 was 1000000. If in 2005 there isan increment of 15% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city atthe end of the year 2007
(A) 985645
(B) 934556
(C) 934578
(D) 994213
(E) 1083875
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 15/100)(1 - 35/100)(1 + 45/100)
= 1083875
E
Answer: (E) 1083875
Question: At what rate percent on simple interest will Rs.900 amount to Rs.950 in 5 years?
(A) 1.11%
(B) 5.93%
(C) 4.33%
(D) 5.33%
(E) 6.33%
Rationale: 50 = (900*5*R)/100
R = 1.11%
ANSWER:A
Answer: (A) 1.11%
Question: A man divides Rs. Among 5 sons,4daughters and 2 nephews .If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews ,how much does each daughter receive?
(A) 200
(B) 300
(C) 400
(D) 500
(E) None of them
Rationale: Let the share of each nephews be Rs.x.
Then,share of each daughter=rs4x;share of each son=Rs.5x;
So,5*5x+4*4x+2*x=8600
25x+16x+2x=8600
=43x=8600
x=200;
Answer is A.
Answer: (A) 200
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides.
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer:A
Answer: (A) 3
Question: A man can row a boat at 20 kmph in still water. If the speed of the stream is 9 kmph, what is the time taken to row a distance of 60 km downstream?
(A) 30/18 hours
(B) 37/13 hours
(C) 80/13 hours
(D) 30/13 hours
(E) 60/29 hours
Rationale: Speed downstream = 20 + 9 = 29 kmph.
Time required to cover 60 km downstream
= d/s = 60/29
= 60/29 hours.
Answer: E
Answer: (E) 60/29 hours
Question: If one-third of one-fourth of a number is 30, then three-tenth of that number is:
A. 35
(A) 23
(B) 87
(C) 108
(D) 54
(E) 01
Rationale: Explanation:
The number is 1/3 of 1/4 is =15 then 1/3 Ã— 1/4 = 30
Number is 360 then 360 Ã— 3/10 = 108
Answer: C
Answer: (C) 108
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 257 m
(B) 268 m
(C) 245 m
(D) 156 m
(E) 150 m
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x
= 150 m.
Answer: E
Answer: (E) 150 m
Question: If there are 4 seats and 3 students, in how many ways can they be seated?
(A) 8
(B) 10
(C) 12
(D) 16
(E) 24
Rationale: The first student has 4 choices, the second student has 3 choices, and the third student has 2 choices. The number of ways to sit is 4*3*2 = 24.
The answer is E.
Answer: (E) 24
Question: What is the next number in the sequence below?
1 4 9 16 25 36 49 64 81 __ ?
(A) 45
(B) 81
(C) 64
(D) 65
(E) 100
Rationale: as the series of numbers are squares of numbers
1^2=1
2^2=4
3^2=9
and so on
therefore 10^2=100
ANSWER:E
Answer: (E) 100
Question: There are 22 Kids in a classroom. 12 Kids are wearing socks and 8 are wearing Shoes. 6 Kids are wearing both.
How many are Bare Feet ?
(A) 10
(B) 2
(C) 4
(D) 5
(E) 8
Rationale: 12 kids wear socks
8 kids wear shoes
6 wear both.
12 â€“ 6 = 6 (wear only socks)
8 â€“ 6 = 2 (wear only shoes)
6 (wear both)
hence, 22 -14 = 8
8 kids are with bare feet.
E
Answer: (E) 8
Question: Out of 12 students in a class, 7 are wearing blue shirts, 3 are wearing green shirts, and 2 are wearing red shirts. Four students are to be selected at random. What is the probability that at least one is wearing a green shirt?
(A) 25/33
(B) 31/44
(C) 41/55
(D) 53/66
(E) 65/77
Rationale: Total possible ways to choose 4 students out of 12 = 12C4 = 495
The number of ways to choose 4 students with no green shirts = 9C4 = 126
P(no green shirts) = 126/495 = 14/55
P(at least 1 green shirt) = 1 - 14/55 = 41/55
The answer is C.
Answer: (C) 41/55
Question: A, B, C, D, E and F are six cities which are collinear in the same order. The distance between any two adjacent cities is equal. A bus starts at A for city F. It takes 25 minutes for the bus to travel from one city to another and stops for 5 minutes at each place. If the bus reaches E at 8:55, then at what time did it reach station B?
(A) 7:25
(B) 7:30
(C) 7:35
(D) 7:40
(E) 7:50
Rationale: Explanation:
Between B and E there are two intermediary stations C and D. For traveling from B to C, from C to D and from D to E it takes 3 * 25 = 75 minutes. At each of C and B it halts of 5 minutes. Hence, the time taken to reach E after starting at B is 85 minutes. i.e. one hour 25 minutes. Hence, it started at 7:30 at B. =>it reached B at 7:25.
ANSWER IS A
Answer: (A) 7:25
Question: The Pinedale bus line travels at an average speed of 60 km/h, and has stops every 5 minutes along its route. Yahya wants to go from his house to the Pinedale Mall, which is 6 stops away. How far away, in kilometers, is Pinedale Mall away from Yahya's house?
(A) 20 km
(B) 30 km
(C) 40 km
(D) 50 km
(E) 60 km
Rationale: Number of stops in an hour: 60/5 = 12
Distance between stops: 60/12 = 5 km
Distance between Yahya's house and Pinedale Mall: 5 x 6 = 30 km
IMO, correct answer is "B."
Answer: (B) 30 km
Question: What number should replace the question mark?
1, 31, 59, 85, 109, ?
(A) 131
(B) 145
(C) 165
(D) 178
(E) 193
Rationale: A
131
Add 30, 28, 26, 24, 22
Answer: (A) 131
Question: The number of bacteria in a petri dish increased by 50 percent every 2 hours. If there were 108 million bacteria in the dish at 3: 00 p.m., at what time were there 32 million bacteria in the dish?
(A) 6: 00 p.m.
(B) 9: 00 p.m.
(C) 6: 00 a.m.
(D) 8: 00 a.m.
(E) 10: 00 a.m.
Rationale: Given:
The number of bacteria in a petri dish increased by 50 percent every 2 hours
There were 108 million bacteria in the dish at 2: 00 p.m
Since the bacteria is increasing by 50% every 2 hours, this means that the number is multiplied by 1.5 every 2 hours.
Required: At what time were there 32 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 32 million and 108 million.
32 * (1.5)^n = 108
(3/2)^n = 108/32 = 27/8 = (3/2)^3
Hence n = 3 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 6
Subtracting 6 hours from 3 PM, we get 9 AM as the answer.
Option B
Answer: (B) 9: 00 p.m.
Question: A man can row 8 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. What is the total distance traveled by the man?
(A) 5.98
(B) 7.98
(C) 7.96
(D) 5.87
(E) 5.82
Rationale: M = 8
S = 1.2
DS = 9.6
US = 6.8
x/9.6 + x/6.8 = 1
x = 3.98
D = 3.98 * 2 = 7.96
Answer:C
Answer: (C) 7.96
Question: On the number line, the number p is twice as many units from -2 as -2 is from 5. If p is less than –2, what is the value of p ?
(A) –16
(B) –10
(C) –6
(D) 10
(E) 14
Rationale: Distance between -2 and 5 = 7
Since number p is twice as many units from -2 as -2 is from 5
, therefore p can be -16 Since , p is less than -2 ,
the value of p = -16
Answer A
Answer: (A) –16
Question: At a certain conference, 62% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 20% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
(A)  18.0%
(B)  62.0%
(C)  79.2%
(D)  77.5%
(E)  82.0%
Rationale: Refer to the table in the attachment:
Let y= No. of members who have paid in Full
20 % members paid in full and did not register in advance = 0.2y
62 % registerd in advance and paid in full.
So if total No. of members = 100, then 62 members paid Full and registered in advance.
Hence total members who paid full amount = 0.2y + 62 =y
0.8y =62
Hence y = 77.5
i.e. 77.5 out of 100 or 77.5 %
Ans. D
Answer: (D)  77.5%
Question: How many two-digit numbers satisfy the following property given below:
The last digit (unit's digit) of the square of the two-digit number is 8?
(A) 4
(B) 12
(C) 15
(D) 16
(E) None of these
Rationale: Explanation:
Any number ending in 8 can never be a perfect square. Hence, the answer is none of these.
ANSWER E
Answer: (E) None of these
Question: Find the odd man out
2880, 482, 96, 24, 8, 4, 4
(A) 482
(B) 96
(C) 24
(D) 8
(E) 4
Rationale: from the right side
4*1=4,
4*2=8
8*3=24
24*4=96
96*5=480 but here given 482 so it's not.
480*6=2880
ANSWER:A
Answer: (A) 482
Question: A prize of $500 is to be distributed among 20 winners, each of whom must be awarded at least $20. If 2/5 of the prize will be distributed to 3/5 of the winners, what is the greatest possible individual award?
(A) $160
(B) $220
(C) $280
(D) $300
(E) $360
Rationale: Total value of the prize =$500
Number of people = 20
2/5 of 500 (=$200) should be distributed among 3/5 of 20 (=12 people ) with each getting $20 each. Remaining money = 500-200 = $300. Now in order to 'maximize' 1 prize, we need to minimise the others and we have been given that each should get $20. Thus, minimising the remaining 7 people (=20-12-1. '-1' to exclude 1 that needs to be maximised) = 7*20=140.
Thus the maximum award can be = 300-140 = $160, hence A is the correct answer.
Answer: (A) $160
Question: A shopkeeper fixes the marked price of an item 35% above its cost price. The percentage of discount allowed to gain 8% is
(A) 18%
(B) 20%
(C) 22%
(D) 24%
(E) None of these
Rationale: Explanation:
Let the cost price = Rs 100
then, Marked price = Rs 135
Required gain = 8%,
So Selling price = Rs 108
Discount = 135 - 108 = 27
Discount% = (27/135)*100 = 20%
Option B
Answer: (B) 20%
Question: William earned $3,200 per month as a
teacher for the ten months from September
to June. Then he took a job as a barista at a
local café, where he earned $2,000 per
month during July and August. What was
his average monthly pay for the 12 months?
(A) $2,400
(B) $2,800
(C) $2,600
(D) $3,000
(E) $2,500
Rationale: E. William earned $3,200 × 10 = $32,000 as a teacher, and he earned $2,000 × 2 = $4,000 as a
barista. So he earned $32,000 + $4,000 = $36,000 over the 12 months. Plug these values into
the formula for the mean:
mean=sum of values/number of values=>36.000/12=3.000
correct answer D)$3.000
Answer: (D) $3,000
Question: What is the largest positive integer n for which 3^n divides 44^44?
(A) 0
(B) 9
(C) 8
(D) 7
(E) 6
Rationale: The digit sum of 44444444 is when remainder obtained 44444444 divided by 9
44444444 = (45−1)44(45−1)44
Each term is a multiple of 9 but the last term which is (−1)44(−1)44 = 1
So the digit sum of 44444444 is 1.
Now the divisibility rule for 3, 9, 27... is the sum of the digits should be divisible by 3, 9, 27 respectively. In each case the digit sum is either multiple of 3 or 9.
So for any value of n > 1, the given expression is not divisible by 3n
Answer:	A
Answer: (A) 0
Question: A fair coin is tossed repeatedly. If heads appears on first 5 tosses what is the probability that tail appears on the next two tosses?
(A) 1/6
(B) 1/5
(C) 1/3
(D) 1/4
(E) 1/6
Rationale: Explanation :
Like mentioned in the question, the coin is fair. So chance of appearing of head and tail on each toss is same and each toss is independent from the previous one. So the chance of appearing tail on the next two tosses is still 1/2 each.
1/2 * 1/2 = 1/4
Answer : D
Answer: (D) 1/4
Question: If 12 men can reap 120 acres of land in 36 days, how many acres of land can 54 men reap in 54 days?
(A) 277
(B) 810
(C) 888
(D) 166
(E) 199
Rationale: 12 men 120 acres 36 days
54 men ? 54 days
120 * 54/12 * 54/36
10 * 54 * 3/2
54 * 15 = 810
Answer: C
Answer: (C) 888
Question: Find the probability that a leap year selected at random will have 53 Sundays
(A) 6/7
(B) 5/7
(C) 4/7
(D) 3/7
(E) 2/7
Rationale: There are 366 days in a leap year: 52 weeks and 2 more days. So, 52 Sundays and 2 days.
These 2 days can be: {Mon, Tue}, {Tue, Wed}, {Wed, Thu}, {Thu, Fri}, {Fri, Sat}, {Sat, Sun} and {Sun, Mon} (7 cases). In order to have 53 Sundays we should have either {Sat, Sun} or {Sun, Mon} case.
The probability of that is 2/7.
Answer: E.
Answer: (E) 2/7
Question: What is the unit digit in {(6374)^1793 x (625)^317 x (341)^491)}?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: Unit digit in (6374)1793 = Unit digit in (4)1793
= Unit digit in [(42)896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Option A
Answer: (A) 0
Question: Find the least number of complete years in which a sum of money put out at 25% compound interest will be more than double of itself?
(A) 3
(B) 6
(C) 9
(D) 4
(E) 3
Rationale: 4 years
Answer: D
Answer: (D) 4
Question: Kramer can pack X boxes of cigarettes per minute. If there are Y boxes of cigarettes in one case, how many cases can Kramer pack in 2 hours?
(A) 60X/Y.
(B) 120X/Y.
(C) 60Y/X.
(D) 120Y/X.
(E) (X + Y)/60.
Rationale: Kramer can pack X boxes per min.
Therefore in 2 hrs(120 mins)he can pack 120X boxes.
If there are Y boxes in one case then then the total number of cases packed by Kramer = 120X/Y
ANSWER:D
Answer: (D) 120Y/X.
Question: If w/x = 1/3 and w/y = 3/4, then (x + y)/y =
(A) 13/4
(B) 6/5
(C) 7/5
(D) 8/5
(E) 9/5
Rationale: W/X = 1/3=>x=3w and W/Y = 3/4=>y=(4/3)w
(X+Y)/Y = (3w+4/3w)/(4/3w)=(13/3w)/(4/3w)=13/4
Correct Option: A
Answer: (A) 13/4
Question: There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ?
(A) 20
(B) 30
(C) 50
(D) 60
(E) 80
Rationale: Explanation:
Let x and y be the number of deer and peacocks in the zoo respectively. Then,
x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
Answer: D
Answer: (D) 60
Question: How many different three-digit multiples of 5 can be composed of digits 1, 2, 3, 4, and 5 if none of the digits is repeated?
(A) 3
(B) 6
(C) 8
(D) 12
(E) 18
Rationale: can you explain your method. i solved it differently
XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 4 possible choices.
X can be any of the 3 possible choices.
4+3+1= 8
C
Answer: (C) 8