mathewhe/aqua_rat huggingface dataset:
Question: There are 50 employees in the office of ABC Company. Of these, 22 have taken an accounting course, 14 have taken a course in finance and 15 have taken a marketing course. Nine of the employees have taken exactly two of the courses and 3 employee has taken all three of the courses. How many of the 50 employees have taken none of the courses?
(A) 4
(B) 9
(C) 8
(D) 5
(E) 14
Rationale: 50 Employees. Counting every different attendand to the courses we have:
Accounting: 22
Finance: 14
Marketing: 15
Which would add up to 51 different attendands, which is not possible.
Now 9 have taken exactly 2 courses, which means that there are 9 less different attendands. Say that 9 of the Finance attentands also attended Accounting.
51-9= 42
3 Person has taken all three courses. As above, we subtract him from the number of different attendands. Since this time the person took all three courses, we have to substract him two times.
42-6= 36.
Answer : E
Answer: (E) 14
Question: A cricket player whose bowling average was 24.85 runs per wicket, takes 5 wicket for 52 runs in a match. Due to this his average decreases by 0.85. What will be the number of wickets taken by him till the last match?
(A) 64
(B) 72
(C) 85
(D) 96
(E) 108
Rationale: Average = Total Runs / Total wickets
Total runs after last match = 24.85w + 52
Total wickets after last match = w + 5
(24.85w + 52) / (w + 5) = 24.85 - 0.85 = 24
w = 80
so total wickets aftr last match = w+5 = 85
ANSWER:C
Answer: (C) 85
Question: A box contains ten bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that at least one bulb is good?
(A) 1/6
(B) 16/625
(C) 609/625
(D) 5/6
(E) 18/263
Rationale: Required probability
= 1 - 16/625
= 609/625
Answer: C
Answer: (C) 609/625
Question: A bag contains 10 balls numbered from 0 to 9. the balls are such that the person picking a ball out of the bag is equally likely to pick anyone of them. A person picked a ball and replaced it in the bag after noting its number. He repeated this process 2 more times. What is the probability that the ball picked first is numbered higher than the ball picked second and the ball picked second is numbered higher than the ball picked third?
(A) 72/100
(B) 3/25
(C) 4/5
(D) 1/6
(E) 1/9
Rationale: Explanation :
Let, the number of the ball picked first =a, second =b and third =c and these three numbers a, b and c are distinct.
Three distinct ball can be picked in (10×9×8) ways.
The order of a, b and c can be as follows:-
(i) a>b>c.
(ii) a>c>b.
(iii) b>c>a.
(iv) b>a>c.
(v) c>a>b.
(vi) c>b>a.
They will occur equal number of times. So, the number of ways in which (a>b>c) are :-
=>1/6 x 10 x 9 x 8.
=>120.
Hence, the required probability is :-
=>120 / (10x10x10).
=>3/25.
Answer : B
Answer: (B) 3/25
Question: In a certain pond, 100 fish were caught, tagged, and returned to the pond. A few days later, 100 fish were caught again, of which 2 were found to have been tagged. If the percent of tagged fish in the second catch approximates the percent of tagged fish in the pond, what is the approximate number of fish in the pond?
(A)  400
(B)  625
(C)  1,250
(D)  2,500
(E)  10,000
Rationale: total fish = x
percentage of second catch = (2/100)*100 = 2%
so, x * 2% = 50
x = 2500 ans. D
Answer: (D)  2,500
Question: P has $21 more than what Q and R together would have had if both B and C had 1/5 of what P has. How much does P have?
(A) $35
(B) $36
(C) $37
(D) $38
(E) $39
Rationale: P = (2/5)*P+21
(3/5)*P=21
P=35
The answer is A.
Answer: (A) $35
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 10% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
(A) 8°
(B) 10°
(C) 18°
(D) 54°
(E) 52°
Rationale: 14% microphotonics;
24% home electronics;
10% food additives;
29% genetically modified microorganisms;
8% industrial lubricants;
100-(14+24+10+29+8)=15% basic astrophysics.
15% of 360° is 54°.
Answer: D.
Answer: (D) 54°
Question: If x = 147, which of the following numbers could be subtracted from x to create a sum that is divisible by 6?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Divisibility rule of 6: A number is divisible by 6 if it is divisible by both 2 and 3
Divisibility rule of 3: A number is divisible by 3 if the sum of the digits is divisible by 3
x = 147. We need to make this number even in order for it to be divisible by 2.
Hence we need to subtract an odd number from it.
Hence left over options are A, C, and E
147 - 1 = 146. Sum of digits = 11.
This is not divisible by 3.
147 - 3 = 144. Sum of digits = 9
This is divisible by 3.
Hence 3 should be subtracted from 147 to make the resultant a multiple of 6.
Correct Option: C
Answer: (C) 3
Question: If log 27 = 1.467, then the value of log 9 is:
(A) 0.978
(B) 0.945
(C) 0.954
(D) 0.958
(E) 0.998
Rationale: log 27 = 1.467
log (3cube ) = 1.467
3 log 3 = 1.467
log 3 = 0.489
log 9 = log(3square ) = 2 log 3 = (2 x 0.489) = 0.978.
Answer: Option A
Answer: (A) 0.978
Question: If the integer x is rounded to the nearest hundred, the result represents a 66 2/3 % increase over the value obtained when x is rounded to the nearest ten. which of the following is a possible value of x?
(A) 64
(B) 67
(C) 99
(D) 133
(E) 147
Rationale: 100= (x-y) + 2/3(x-y)
300=5(x-y)
x-y =60
64 rounded to nearest tenth will result in 60.
Answer A
Answer: (A) 64
Question: How many numbers between 1 and 100 are divisible by 7 ?
(A) 9
(B) 11
(C) 17
(D) 14
(E) 12
Rationale: No. of divisible by 7 7, 14 --------- 98, n = a + (N - 1)d
98 = 7 + (N - 1) 7, 98 = 7 + 7N - 7
98/7= N = 14
Answer:D
Answer: (D) 14
Question: A sum of money is to be divided among Ann, Bob and Chloe. First, Ann receives $4 plus one-half of what remains. Next, Bob receives $4 plus one-third of what remains. Finally, Chloe receives the remaining $32. How much money N did Bob receive?
(A) 20
(B) 22
(C) 24
(D) 26
(E) 52
Rationale: Notice that we need not consider Ann's portion in the solution. We can just let K = the money REMAINING after Ann has received her portion and go from there.
Our equation will use the fact that, once we remove Bob's portion, we have $32 for Chloe.
So, we getK - Bob's $ = 32
Bob received 4 dollars plus one-third of what remained
Once Bob receives $4, the amount remaining is K-4 dollars. So, Bob gets a 1/3 of that as well.
1/3 of K-4 is (K-4)/3
So ALTOGETHER, Bob receives4 + (K-4)/3
So, our equation becomes:K -[4 + (K-4)/3 ]= 32
Simplify to get: K - 4 - (K-4)/3 = 32
Multiply both sides by 3 to get: 3K - 12 - K + 4 = 96
Simplify: 2K - 8 = 96
Solve: K = 52
Plug this K-value intoK - Bob's $ = 32to get: 52 - Bob's $ = 32
So, Bob's $ N= 20
Answer:
B
Answer: (B) 22
Question: If d is a positive even integer, and n and m are consecutive integers, then (n - m)^d/(m - n)d =
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: d= +ve even integer
Since,n and m are consecutive integers , their difference will be 1
((n-m)^d)/((m-n)d)= ((n-m)/(m-n))^d = (-1)^d
Since we are raising the difference of n and m to power d , which is even , the answer will be 1 .
Answer D
Answer: (D) 1
Question: A sum of $800 amounts to $920 in 3 years at simple interest. If the interest rate is increased by 3% it would amount to how much ?
(A) $506
(B) $774
(C) $992
(D) $854
(E) $1021
Rationale: S.I = 920-800 = 120
P = $800
T = 3 years
R = 100*120 / 800*3 = 5%
New rate = 5+3 = 8%
New S.I. = 800*8*3/100 = $192
New amount = 800+192 = $992
Answer is C
Answer: (C) $992
Question: The ratio, by weight, of coffee to sugar to water in a pot of coffee is 5:2:20. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is tripled. If the altered pot of coffee contains 8 grams of sugar, how many grams of water does it contain after alteration?
(A) 12
(B) 12.5
(C) 13
(D) 13.5
(E) 14
Rationale: The new ratio of coffee to sugar is 2.5:2
The new ratio of coffee to water is 15:20.
The new ratio of coffee to sugar to water is 15:12:20.
If there are 8 grams of sugar, then there are (21/12)*8=14 grams of water.
The answer is E.
Answer: (E) 14
Question: Expenditures of a Company (in Lakh Rupees) per Annum Over the given Years.
Year	Item of Expenditure
Salary	Fuel and Transport	Bonus	Interest on Loans	Taxes
1998	288	98	3.00	23.4	83
1999	342	112	2.52	32.5	108
2000	324	101	3.84	41.6	74
2001	336	133	3.68	36.4	88
2002	420	142	3.96	49.4	98
Total expenditure on all these items in 1998 was approximately what percent of the total expenditure in 2002?
(A) 62%
(B) 69.45%
(C) 70%
(D) 71%
(E) 72%
Rationale: Required percentage
=	[	(288 + 98 + 3.00 + 23.4 + 83)	x 100	]	%
(420 + 142 + 3.96 + 49.4 + 98)
=	[	495.4	x 100	]	%
713.36
~= 69.45%.
B)
Answer: (B) 69.45%
Question: The area of sector of a circle whose radius is 12 metro and whose angle at the center is 54Â° is?
(A) 52.6
(B) 52.9
(C) 67.9
(D) 52.1
(E) 52.2
Rationale: 54/360 * 22/7 * 12 * 12 = 67.9 m2
Answer: C
Answer: (C) 67.9
Question: What is 1! + 2! + ... + 10! ?
(A) 4,037,910
(B) 4,037,913
(C) 4,037,915
(D) 4,037,916
(E) 4,037,918
Rationale: All options have different Unit digit so calculating unit digit of the sum above will suffice
Unit digit of (1! + 2! + 3! + 4! + 5! + 6!+... + 10!) = 1 + 2+ 6 + 4 + 0 + 0 + 0 + 0+ 0 + 0 = Unit digit 3, Hence
every Factorial of an integer greater than 4 will have Unit digit 0 as it will be a multiple of 10
Answer: option B
Answer: (B) 4,037,913
Question: Apples are bought at 11 for a $ and an equal number more at 9 a $. If these are sold at 10 for a $, find the loss or gain percent?
(A) 5% loss
(B) 7% loss
(C) 3% loss
(D) 2% loss
(E) 1% loss
Rationale: E
1% loss
Answer: (E) 1% loss
Question: There are two groups of students in the sixth grade. There are 20 students in group A, and 80 students in group B. If, on a particular day, 20% of the students in group A forget their homework, and 15% of the students in group B forget their homework, then what percentage of the sixth graders forgot their homework?
(A) 13%
(B) 14%
(C) 15%
(D) 16%
(E) 17%
Rationale: Number of students in group A = 20
students who forget homework in group A = 20 % of 20 = 4 students
Number of students in group B = 80
students who forget homework in group B = 15 % of 80 = 12 students
Total number of students = 20 + 80 = 100
students who forgot homework = 4 + 12 = 16 students
percentage of students who forget homework = 16/100 * 100 = 16%
Answer: D
Answer: (D) 16%
Question: What is the value of (44444445*88888885*44444442+44444438)/44444444^2
(A) 88888883
(B) 88888827
(C) 16992677
(D) 88888237
(E) 88888182
Rationale: Ans: A
Let x = 44444444
(x+1)×(2x−3)×(x−2)+(x−6)x2(x+1)×(2x−3)×(x−2)+(x−6)x2
(x2−x−2)×(2x−3)+(x−6)x2(x2−x−2)×(2x−3)+(x−6)x2
2x3−2x2−4x−3x2+3x+6+x−6x22x3−2x2−4x−3x2+3x+6+x−6x2
2x3−5x2x2=2x−52x3−5x2x2=2x−5
Substituting the value of x in 2x - 5, we get 88888883
Answer:A
Answer: (A) 88888883
Question: Find average speed if a man travels at speed of 20km/hr up and 26km/hr dawn at an altitude of 240m.
(A) 25.8
(B) 26.8
(C) 22.6
(D) 28.8
(E) 29.8
Rationale: avg speed=2*x*y/(x+y)
=2*20*26/(20+26)=22.6
ANSWER:C
Answer: (C) 22.6
Question: Find the remainder Y when 12^190 is divided by 1729 ?
(A) 12
(B) 1
(C) 1728
(D) 1717
(E) 4
Rationale: 12^(190) can be written as. ((12^3)^63)* 12. 12^3 when divided by 1729 gives a remainder Y -1. so in the numerator we have -12. Now acccording to remainder theorm the answer will be 1729-12=1717.D
Answer: (D) 1717
Question: What is the perimeter of a square with area 9p^2/36 ?
(A) 3p/4
(B) 3p^2/4
(C) 2p
(D) 3p^2
(E) 4p/3
Rationale: Area of square, (side)^2 = (3p/6)^2
Therefore side of the square = 3p/6
Perimeter of square = 4*side = 4* (3p/6) = 2p
Answer is C.
Answer: (C) 2p
Question: Find the simple interest on Rs.500 for 9 months at 6 paisa per month?
(A) 238
(B) 270
(C) 987
(D) 167
(E) 121
Rationale: I = (500*9*6)/100 = 270
Answer:B
Answer: (B) 270
Question: A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
(A) 600
(B) 267
(C) 132
(D) 277
(E) 161
Rationale: Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600
Answer:A
Answer: (A) 600
Question: Two vessels A and B contain spirit and water in the ratio 5 : 2 and 7 : 6 respectively. Find the ratio in which these mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ration 8 : 5?
(A) 4 : 3
(B) 3 : 4
(C) 5 : 6
(D) 7 : 9
(E) None
Rationale: Let the C.P. of spirit be Re. 1 litre.
Spirit in 1 litre mix. of A = 5/7 litre, C.P. of 1 litre mix. in A = Re. 5/7
Spirit in 1 litre mix. of B = 7/13 litre, C.P. of 1 litre mix. in B = Re. 7/13
Spirit in 1 litre mix. of C = 8/13 litre, Mean price = Re. 8/13.
By the rule of alligation, we have:
Required ratio = 1/13 : 9/91 = 7 : 9.
Answer D
Answer: (D) 7 : 9
Question: Three numbers are in the ratio of 2 : 3 : 4 and their L.C.M. is 240. Their H.C.F. is:
(A) 30
(B) 20
(C) 40
(D) 60
(E) 70
Rationale: Explanation:
Let the number be 2x, 3x and 4x
LCM of 2x, 3x and 4x = 12x
12x = 240
=> x = 240/12 = 20
HCF of 2x, 3x and 4x = x = 20
Answer: Option B
Answer: (B) 20
Question: A box contains 40 balls, numbered from 1 to 40. If three balls are selected at random and with replacement from the box, what is the probability that the sum of the three numbers on the balls selected from the box will be odd?
(A) 1/4
(B) 3/8
(C) 1/2
(D) 5/8
(E) 3/4
Rationale: I don't think order matters in this case, because 2 + 2 + 1 = 2 + 1 + 2
My answer is: 1/4
A
Answer: (A) 1/4
Question: How many even prime numbers are there less than 50?
(A) 15
(B) 1
(C) 2
(D) 16
(E) 17
Rationale: 2 is the only even prime number
Answer is B
Answer: (B) 1
Question: The total number of plums that grow during each year on a certain plum tree is equal to the number of plums that grew during the previous year, less the age of the tree in years (rounded down to the nearest integer). During its 4th year, the plum tree grew 50 plums. If this trend continues, how many plums will it grow during its 6th year?
(A) 36
(B) 41
(C) 38
(D) 40
(E) 42
Rationale: 1st year : 0-1 (age), we take age = 0 (as the question says that we have to(rounded down to the nearest integer))
2ndyear : 1-2 (age), we take age = 1
3rd year : 2-3 (age), we take age = 2
4th year : 3-4 (age), we take age = 3
5th year : 4-5 (age), we take age = 4
6th year : 5-6 (age), we take age = 5
Thus for the 4th year = 50,
5th year = 50 -4 = 46
6th year = 46-5 = 41
The correct answer is B.
Answer: (B) 41
Question: The number of singles that a baseball player hit increased 18 percent from her first season to her second season, and the number of doubles that she hit in the same time period decreased by 6 percent. If the total number of singles and doubles that she hit increased 3 percent from her first season to her second season, what is the ratio of the number of singles she hit in her first season to the number of doubles she hit in her first season?
(A) 1:3
(B) 4:5
(C) 1:5
(D) 2:5
(E) 3:5
Rationale: Soln:-
1.18S + 0.94D = 1.03[S + d]
0.15S = 0.09D
S/D = 3/5
ANSWER:E
Answer: (E) 3:5
Question: Jill, who lives in City C, plans to visit 3 different cities, M, L, and S. She plans to visit each city exactly once and return to City C after the 3 visits. She can visit the cities in any order. In how many different orders can she visit the 3 cities?
(A) 3
(B) 6
(C) 8
(D) 9
(E) 12
Rationale: 3! = 6
M	L	S	C
M	S	L	C
L	M	S	C
L	S	M	C
S	M	L	C
S	L	M	C
She can visit the cities in any order. Number of ways of arranging the three cities is 3! = 6 ways. Hence B.
Answer: (B) 6
Question: What approximate value should come in place of the question mark (?) in the following equation?
39.05 × 14.95 – 27.99 × 10.12 = (36 + ?) × 5
(A) 22
(B) 29
(C) 34
(D) 32
(E) 25
Rationale: Solve using approximation
Answer E
Answer: (E) 25
Question: If 4 (A's capital) = 6 (B's capital) = 10 (C's capital), then out of a profit of Rs. 372, C will receive
(A) 60
(B) 51
(C) 900
(D) 72
(E) 271
Rationale: Explanation:
Let 4A = 6B = 1OC = k. Then, A = k/4, B = k/6, and C =k/10 .
A : B :C = k/4 : k/6 : k/10 = 15 : 10 : 6.
Hence, C's share (372 * 6/31) = Rs, 72.
Answer: D) Rs.72
Answer: (D) 72
Question: If y exceeds x by 25%, then x is less than y by?
(A) 22%
(B) 67%
(C) 20%
(D) 16%
(E) 11%
Rationale: X=100	y=125
125--------25
100--------? => 20%
Answer: C
Answer: (C) 20%
Question: In a 500 member association consisting of men and women, exactly 20% of men and exactly 50 % women are homeowners. What is the least number of members who are homeowners?
(A) 149
(B) 147
(C) 101
(D) 143
(E) 141
Rationale: Solution simple
Out of 500 20% are male i.e 100 and 50% are female i.e 250 , so total homeowner is 350.
Now min number homeowner is 100 and max is 250 so question ask us to find least and 101 has least value among all option.
So ans is 101.
Ans: C
Answer: (C) 101
Question: 7/9 of 3/5 of a number is greater than 2/9 of 5/6 of the same number by 152. What is half of that number?
(A) 165
(B) 195
(C) 240
(D) 270
(E) 315
Rationale: Let no. be x
7/9*3/5*x - 2/9*5/6*x =152
by further solving
21x/45- 10x/54=152
114x/405=152
x=540
we have to find x/2
=540/2=270
ANSWER:D
Answer: (D) 270
Question: In a class of 120 students, 25 did not opt for math. 10 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science?
(A) 63
(B) 95
(C) 77
(D) 87
(E) 48
Rationale: 120 students total
25 did not opt for math
10 did not opt for science
2 did not opt for either
Total of 95 students in math and 8 did not opt for sci but did for math
95-8=87
87 students of the class opted for both math and science
Answer:
D. 87
Answer: (D) 87
Question: The number N is 6,2X4, where X represents the ten's digit. If N is divisible by 9, what is the value of X?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 6
Rationale: Integer is divisible by 9 - Sum of digits is divisible by 9
Answer: E
Answer: (E) 6
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 128. The dividend from the stock is:
(A) 8%
(B) 6%
(C) 9%
(D) 10%
(E) 11%
Rationale: Rs 1552 income = Rs 128
By investing Rs 97 income = 128/1552*97 = Rs 8
Divdend = 8%
ANSWER A
Answer: (A) 8%
Question: A Scooter is sold for Rs. 65000, a shop keeper gains 25%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
(A) 25%
(B) 12.5%
(C) 22.5%
(D) 15%
(E) 36%
Rationale: Explanation:
Marked price = Rs. 65000
C.P. = 100/125 * 65000 = Rs. 52000
Sale price = 90% of Rs. 65000 = Rs. 58500
Required gain % = 650/52000 * 100 = 12.5%.
Answer: B
Answer: (B) 12.5%
Question: How many 6 digit number can be formed from the digits 1, 2, 3, 4, 5, 6 which are divisible by 4 and digits are not repeated?
(A) 192
(B) 122
(C) 140
(D) 242
(E) None
Rationale: Solution
For the number to be divisible by 4, the last two digits must be any of 12, 24, 16, 64, 32, 36, 56 and 52. The last two digit places can be filled in 8 ways. Remaining 3 places in 4P3 ways.
Hence no. of 5 digit nos. which are divisible by 4 are 24 × 8 = 192
Answer A
Answer: (A) 192
Question: The current birth rate per thousand is 50, where as corresponding death rate is 10 per thousand. The net growth rate in terms of population increase in percent is given by?
(A) 2%
(B) 3%
(C) 4%
(D) 6%
(E) 8%
Rationale: Net growth on 1000 = 50-10 = 40
Net growth on 100 = 40*100/1000 = 4%
Answer is C
Answer: (C) 4%
Question: A machine puts c caps on bottles in m hours. How many hours will it take to put caps on b bottles?
(A) 60bm/c
(B) bm/60c
(C) bc/60m
(D) bm/c
(E) b/60cm
Rationale: A machine puts c caps on bottles in m minutes.
So, the machine puts 1 cap in m/c minutes
To put caps on b bottles, the machine will take bm/c hours
Answer : D
Answer: (D) bm/c
Question: If 5% more is gained by selling an article for Rs. 350 than by selling it for Rs. 320, the cost of the article is
(A) 289
(B) 231
(C) 200
(D) 288
(E) 600
Rationale: Explanation:
Let C.P. be Rs. x.
Then, 5% of x = 350 - 320 = 30
x/20 = 30 => x = 600
Answer: E
Answer: (E) 600
Question: How many of the positive factors of 24 are not factors of 26
(A) 2
(B) 3
(C) 4
(D) 1
(E) 6
Rationale: factors of 24 - 1, 2, 3, 4, 6, 8, 12,24
factors of 26 -1, 2, 13, 26
Comparing both, we have 6 factors of 24 which are not factors of 26- 3, 4, 6, 8, 12,24
Answer: E
Answer: (E) 6
Question: Calculate the HCF of 64, 318, 250
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: Explanation:
Lets solve this question by factorization method.
64=2 x 2 x 2 x 2 x 2 x 2,
318=2 × 3 × 53,
250=2 × 5 × 5 × 5
So HCF will be minimum term present in all three, i.e.
2×32=18
Answer: Option E
Answer: (E) 2
Question: A certain cube floating in a bucket of water has between 80 and 90 percent of its volume below the surface of the water. If between 6 and 13 cubic centimeters of the cube's volume is above the surface of the water, then the length of a side of the cube is approximately
(A) 4
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: If sides are 7, vol=7^3=343
80%= 274.4, 90%=308.7
so vol above water, between 68.6 and 34.3 -->too big
If side are 4, vol = 64
80%=51.2, 90%=57.6
vol above water between 12.8 and 6.4
So 4 should be the answer.
Check option C,
If sides are 5, vol = 125
80%= 100, .90%=112.5
vol above water between 12.5-25
(Sides are 4 cubic centimeters)
A
Answer: (A) 4
Question: the radius of the circle is reduced from 5cm to 4cm then the % change of area .
(A) 36%
(B) 37%
(C) 35%
(D) 38%
(E) 39%
Rationale: for 5cm -> pi*r^2 --> 3.14 * 5 ^ 2 -> 78.539
for 4cm -> pi*r^2 --> 3.14 * 4 ^ 2 -> 50.265
%change -> (1- 50.265/78.539)*100= 36
ie 36%
ANSWER:A
Answer: (A) 36%
Question: Sum of the squares of three numbers is 138 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 22
(C) 25
(D) 27
(E) 29
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 138 + 2* 131
a + b + c = √400 = 20
A
Answer: (A) 20
Question: Balls of equal size are arranged in rows to form an equilateral triangle. the top most row consists of one ball, the 2nd row of two balls and so on. If 1104 balls are added, then all the balls can be arranged in the shape of square and each of the sides of the square contain 8 balls less than the each side of the triangle did. How many balls made up the triangle?
(A) 2145
(B) 2209
(C) 2878
(D) 1210
(E) 1560
Rationale: As expected, this question boils down to 2 equation,
Consider total number of Balls in Triangle = T and number of balls in last row = x.
1+2+3+...+x = T
x(x+1)/2 = T ----(a)
As mentioned in the question, side of a square will be (x-8) and total number of Balls in square will be (T+1104)
(x-8)^2 = T+1104 -----(b)
Now the hardest part of the question will be to solve these 2 equations and this looks like time consuming BUT the easy way will be plug and play. Also, we've to find a value of T (from 5 optiosn given below) which can make a square of a a number. One we know this, it will be a cake walk.
We can see that option A fits this criteria in eq (b). Add - 2145+1104 = 3249 = 57^2 = (x-8)^2 Hence, x = 65.
Cross check by putting in eq (a) = x(x+1)/2 = T = > 65*66/2=2145
Hence, answer is A.
Answer: (A) 2145
Question: Find the probability that a number selected from numbers 1, 2, 3,..., 30 is a prime number, when each of the given numbers is equally likely to be selected?
(A) 10/30
(B) 1/30
(C) 8/30
(D) 3/30
(E) 7/30
Rationale: Let X be the event of selecting a prime number.
X = {2, 3, 5, 7, 11, 13, 17, 19, 23,29}
n(X) = 10,
n(S) = 30
Hence, the required probability is 10/30.
ANSWER:C
Answer: (C) 8/30
Question: The price of a car is marked at $10,000. If the car has successive discounts of 25%, 20% and 10%, then at what price does a customer buy the car?
(A) $4600
(B) $4800
(C) $5000
(D) $5200
(E) $5400
Rationale: 0.9*0.8*0.75*10000 = $5400
The answer is E.
Answer: (E) $5400