mathewhe/aqua_rat huggingface dataset:
Question: Out of 15 students studying in a class, 7 are from Maharashtra, 5 are from Karnataka and 3 are from Goa. Four students are to be selected at random. What are the chances that at least one is from Karnataka?
(A) 12⁄13
(B) 11⁄13
(C) 10⁄15
(D) 1⁄15
(E) None of these
Rationale: Total possible ways of selecting 4 students out of 15 students = 15C4 = 15×14×13×12 /1×2×3×4=1365
The no. of ways of selecting 4 students in which no student belongs to Karnataka = 10C4
∴ Hence no. of ways of selecting at least one student from Karnataka = 15C4 – 10C4 = 1155
∴ Probability = 1155⁄1365 = 77⁄91 = 11⁄13
Answer B
Answer: (B) 11⁄13
Question: In a series of six consecutive even numbers, the sum of the third and sixth numbers is 30. What are the third and sixth number respectively?
(A) 10,16
(B) 8,14
(C) 16,22
(D) 14,20
(E) 12, 18
Rationale: Let the numbers be x, x + 2, x + 4, x + 6, x + 8 and x + 10.
Given (x + 4) + (x + 10) = 30
=> 2x + 14 = 30 => x = 8
The third number = x + 4 = 8 + 4 = 12.
The sixth number = x + 10 = 8 + 10 = 18.
Answer: E
Answer: (E) 12, 18
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
(A) 12,7
(B) 12,9
(C) 10,5
(D) 11,6
(E) 15,4
Rationale: x â€“ y = 5
4x â€“ 6y = 6
x = 12 y = 7
ANSWER A
Answer: (A) 12,7
Question: In a box, there are 5 blue, 8 white and 3 yellow bulbs. One bulb is picked up randomly. What is the probability that it is neither white nor blue?
(A) 3/16
(B) 5/16
(C) 8/32
(D) 2/32
(E) 9/32
Rationale: Total number of bulbs = (5 + 8 + 3) = 16.
Let E = event that the bulb drawn is neither white nor blue = event that the bulb drawn is yellow.
Therefore, P(E)=3/16
ANSWER:A
Answer: (A) 3/16
Question: Find compound interest on Rs. 8000 at 15% per annum for 2 years 4 months, compounded annually
(A) 2109
(B) 3109
(C) 4109
(D) 6109
(E) 1109
Rationale: Time = 2 years 4 months = 2(4/12) years = 2(1/3) years.
Amount = Rs'. [8000 X (1+(15/100))^2 X (1+((1/3)*15)/100)]
=Rs. [8000 * (23/20) * (23/20) * (21/20)]
= Rs. 11109. .
:. C.I. = Rs. (11109 - 8000) = Rs. 3109. Answer: B
Answer: (B) 3109
Question: If x is the product of the positive integers from 1 to 8, inclusive, and if i, k, m, and p are positive integers such that x=2^i∗3^k∗5^m∗7^p, then i + k + m + p =
(A) 4
(B) 7
(C) 8
(D) 11
(E) 12
Rationale: Here the idea is to go expressing each factor from one to eight, decomposed into its primes:
1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 = 1 * 2 * 3 *(2*2) * 5 +(2*3) * 7 *(2*2*2) = 2 ^ 7 * 3 ^ 2 * 5 ^ 1 * 7 ^ 1
Then
i = 7
k = 2
m = 1
p = 1
i + k + m + p = 11
Correct answer D
Answer: (D) 11
Question: There are 14 points in a given plane, no three of which are on the same line. If one of the points is represented as 'A', then how many triangles can be determined with the 14 points that contain the point A?
(A) 78
(B) 105
(C) 182
(D) 210
(E) 455
Rationale: Any 2 points out 13 points will create triangle with third point A, so the answer is 13C2=78.
Answer: A.
Answer: (A) 78
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.18
(B) 7.12
(C) 7.16
(D) 7.15
(E) 7.11
Rationale: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer:D
Answer: (D) 7.15
Question: The ratio between the present ages of A and B is 4.5:3 respectively. The ratio between A's age 4 years ago and B's age 4 years hence is 1:1. What is the ratio between A's age 4 years hence and B's age 4 years ago?
(A) 3:4
(B) 3:0
(C) 3:1
(D) 7:3
(E) 3:7
Rationale: Let the present ages of A and B be 4.5x and 3x years respectively.
Then, (4.5x - 4)/(3x + 4) = 1/1
1.5x = 8 => x = 5.33
Required ratio = (5x + 4):(3x - 4) = 28:12 = 7:3.Answer: D
Answer: (D) 7:3
Question: The area of a square is 4225 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
(A) 5:28
(B) 5:19
(C) 5:12
(D) 5:13
(E) 41:130
Rationale: Let the length and the breadth of the rectangle be l cm and b cm respectively. Let the side of the square be a cm.
a2 = 4225
a = 65
L = 2a and b = a - 24
b : l = a - 24 : 2a = 41 : 130
Answer:E
Answer: (E) 41:130
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 180 gm mixture, 36 gms of pure milk is added, what would be the percentage of milk in the mixture formed?
(A) 83.37%
(B) 83.93%
(C) 83.38%
(D) 83.23%
(E) 83.33%
Rationale: Percentage of milk in the mixture formed
= [80/100 (180) + 36] / (180 + 36) * 100% = (144 + 36)/216 * 100%
= 5/6 * 100% = 83.33%.
Answer:E
Answer: (E) 83.33%
Question: The average of 10 numbers is zero. Of them, How many of them may be greater than zero, at the most?
(A) 6
(B) 7
(C) 10
(D) 8
(E) 9
Rationale: Average of 10 numbers = 0
=> Sum of 10 numbers/10=0
=> Sum of 10 numbers = 0
Hence at the most, there can be 9 positive numbers.
(Such that if the sum of these 9 positive numbers is x, 10th number will be -x)
ANSWER:E
Answer: (E) 9
Question: By selling an article at Rs.500, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
(A) s.600
(B) s.480
(C) s.300
(D) s.450
(E) s.550
Rationale: SP = 500
Profit = 25%
CP = (SP)*[100/(100+P)]
= 500 * [100/125]
= 400
Loss = 25% = 25% of 400 = Rs.100
SP = CP - Loss = 400 - 100 = Rs.300
ANSWER:C
Answer: (C) s.300
Question: What percent is 50 gm of 1 kg?
(A) 1.5 %
(B) 0.5 %
(C) 2.5 %
(D) 3.5 %
(E) 5 %
Rationale: 1 kg = 1000 gm
50/1000 × 100 = 5000/1000
=5/1 = 5 %
E)
Answer: (E) 5 %
Question: A certain bus driver is paid a regular rate of $16 per hour for any number of hours that does not exceed 40 hours per week. For any overtime hours worked in excess of 40 hours per week, the bus driver is paid a rate that is 75% higher than his regular rate. If last week the bus driver earned $920 in total compensation, how many total hours did he work that week?
(A) 36
(B) 40
(C) 44
(D) 50
(E) 52
Rationale: For 40 hrs = 40*16=640
Excess = 920-640=280
For extra hours =.75(16)=12+16=28
Number of extra hrs =280/28=70/7=10
Total hrs =40+10=50
Answer D 50
Answer: (D) 50
Question: A and B started a business investing Rs. 90,000 and Rs 30,000 respectively. In what ratio the profit earned after 2 years be divided between A and B respectively?
(A) 9:2
(B) 3:1
(C) 18:20
(D) 18:4
(E) 17:4
Rationale: A: B = 90000 : 30000
= 9 : 3
= 3 : 1
ANSWER:B
Answer: (B) 3:1
Question: x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 4 will be equal to:
(A) 3
(B) 6
(C) 1/9
(D) 1/3
(E) 9/16
Rationale: Explanation :
Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.
.'. x = 9/y^2
=> x =9 /4^2 = 9/16
Answer : E
Answer: (E) 9/16
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 198.The amount of the bill is
(A) Rs. 1386
(B) Rs. 1764
(C) Rs. 1650
(D) Rs. 2268
(E) None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.198.
∴ x 16 x9/ 12x 1/100}= 198 or x = 1650.
∴ P.W. = Rs. 1650.
Answer C
Answer: (C) Rs. 1650
Question: What is the next number in the sequence : 14,19,29,40,44,52,59,73 __?
(A) 90
(B) 85
(C) 81
(D) 85
(E) 83
Rationale: next no. = previous + (sum of digits)
14 + (1+4) = 19
19 + (1+9) = 29
29 + (2+9) = 40
40 + (4+0) = 44
44 + (4+4) = 52
52 + (5+2) = 59
59 +(5+9) = 73
73 + (7+3) = 83
ANSWER:E
Answer: (E) 83
Question: A person starts writing all 4 digit numbers .How many times had he written the digit 3?
(A) 3700
(B) 3800
(C) 3900
(D) 4000
(E) 4100
Rationale: _ _ _ 3 = 9*10*10
_ _ 3 _ = 9*10*10
_ 3 _ _ = 9*10*10
3 _ _ _ = 10*10*10
900+900+900+1000=3700
ANSWER:A
Answer: (A) 3700
Question: The salaries of A, B and C are in the ratio 1:3:4. If the salaries are increased by 5%, 10% and 15% respectively, then the increased salaries will be in the ratio
(A) 20:66:95
(B) 21:66:96
(C) 21:66:92
(D) 19:66:92
(E) None
Rationale: Solution: Let A's Salary = Rs. 100
Then, B's Salary = Rs. 300
And, C's Salary = Rs 400
Salary has given in 1:3:4 ratio.
Now,
5% increase in A's Salary,
A's new Salary = (100 + 5% of 100) = Rs. 105.
B's Salary increases by 10%, Then,
B's new Salary = (300 + 10% of 200) = Rs. 330.
C's Salary increases by 15%,
C's new Salary = (400 + 15% of 400) = Rs. 460.
Then, ratio of increased Salary,
A:B:C = 105:330:460 = 21:66:92.
Alternative
100(A's salary)===5%↑===> 105(A's increased salary);
300 (B's salary)===10%↑===>330 (B's increased salary);
400 (C's salary)===15%↑===> 460 (C's increased salary).
Ratio of their increased salary = 105:330:480 = 21:66:92
Answer: Option C
Answer: (C) 21:66:92
Question: If the average (arithmetic mean) of a and b is 45 and the average of b and c is 50, what is the value of c âˆ’ a?
(A) 25
(B) 10
(C) 90
(D) 14
(E) It cannot be determined from the information given
Rationale: the arithmetic mean of a and b =(a+b)/2=45 -- a+b=90 --1
similarly for b+c=100 --2
subtracting 1 from 2 we have
c-a=10;
ANSWER:B
Answer: (B) 10
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:8
(C) 1:1
(D) 1:6
(E) 1:3
Rationale: T = 192/32 = 6 h
T = 6 - 3 = 3
Time Ratio = 6:3 = 2:1
Speed Ratio = 1:2
Answer: A
Answer: (A) 1:2
Question: Find the least value of 'a' so that 365a16 is divisible by 8.
(A) 9
(B) 8
(C) 0.
(D) 2
(E) 1
Rationale: Explanation:
Given, number is divisible by 8 only if 'a16' is divisible by 8.
.: Least value of a is '0'.
Answer: Option C
Answer: (C) 0.
Question: A mixture contains milk and water in the ratio 5:2. On adding 10 liters of water, the ratio of milk to water becomes 5:3. The quantity of milk in the original mixture is?
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: milk:water = 5:2
5x : 2x + 10 = 5 : 3
3[5x] = 5[2x + 10]
15x = 10x + 50
15x - 10x = 50
x = 10
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7x = 70
Short cut method:
milk:water = 5 :2
after adding 10 liters of water
milk:water = 5 :3
milk is same but water increse 10liters then the water ratio is increse 1 parts
1 part -----> 10 liters
The quantity of milk in the original mixture is = 5 : 2 = 5 + 2 = 7
7 parts -----> 70 liters (Answer is = 70)
Short cut method - 2 : for Only milk problems
milk : water
5 : 2
5 : 3
milk ratio same but water ratio 1 part incress per 10 liters
1 part of ratio -------> 10 liters
7 part of ratio -------> 70 liters
C)
Answer: (C) 50
Question: If x,y ,and z are positive real numbers such that x(y+z) = 132, y(z+x) =152 , and z(x+y) = 180, then xyz is
(A) 40
(B) 60
(C) 160
(D) 100
(E) 120
Rationale: xy+xz = 132 --------------------------------------1)
yz+yx = 152---------------------------------------2)
xz+zy = 180---------------------------------------3)
Re-writing equation 3 as follows:
xz+zy = 152 + 28
xz+zy = yz+yx + 28
xz = yx + 28 ............... (4)
Adding (1)(4)
2xz = 160
xz = 80
xyz has to be multiple of 80,only 160 fits in
Answer = C
Answer: (C) 160
Question: One-third of Rahul’s savings in National Savings Certificate is equal to one-half of his savings in Public Provident Fund. If he has Rs. 2,00,000 as total savings, how much has he saved in Public Provident Fund ?
(A) Rs. 30,000
(B) Rs. 50,000
(C) Rs. 80,000
(D) Rs. 90,000
(E) None
Rationale: EXPLANATION
Let savings in N.S.C and P.P.F. be Rs. x and Rs. (200000 – x) respectively. Then,
1/3x=1/2(200000-x)
=> x/3 + x/2 = 100000
=> 5x/6 = 100000
=> x= 100000 x 6 /5= 120000
Savings in Public Provident Fund = Rs. (200000 – 120000) = Rs. 80000
Answer C
Answer: (C) Rs. 80,000
Question: A shop sells floor tiles at Rs 48 per square meter. A building contractor employs a machine that polishes the tiles that damages 10% of the total number of tiles which cannot be used any more. Calculate the amount that needs to be paid by contractor to tile shop owner, if the hall is of a square shape and has a perimeter of 400 meters?
(A) Rs 4,00,000
(B) Rs 5,00,000
(C) Rs 5,28,000
(D) Rs 3,65,000
(E) Rs 3,75,000
Rationale: 4 sides of a square then 400/4=100
area of the hall 100*100=10000
10% damaged so 10000*110/100=11000
48 per square meter then 48*11000=528000
ANSWER:C
Answer: (C) Rs 5,28,000
Question: In what ratio must the rice at Rs.3.20/kg be combined with rice at Rs.2.90/kg so that the combination becomes of worth Rs.3.08/kg ?
(A) 3:2
(B) 5:3
(C) 7:3
(D) 7:5
(E) 8:5
Rationale: Explanation :
Given
i. C.P of a kg quantity of I kind (p) = 3.20
ii. C.P of a kg quantity of II kind (p) = 2.90
iii. Mean rice price (p) = 3.08
iv. d – m = 3.08 – 2.90 = 0.18
v. m – c = 3.20 – 3.08 = 0.12
Therefore, Needed ratio = 0.18 : 0.12 = 3 : 2
Answer : A
Answer: (A) 3:2
Question: 1/3th of the passengers got down at first stop and 30 people got into the bus, 1/4th of the passengers got down at second stop and 12 people got into the bus.In last stop 84 people got down from the bus. What is the initial capacity of the bus?
(A) 98
(B) 99
(C) 97
(D) 96
(E) 95
Rationale: Let x be the no of initial passenger
no of passengr left in 1st stop (2x/3)+30
no of passenger in the 2nd stop 3/4((2x/3)+30) + 12
which is equal to 84 (passngr on last stop)
so final eqn....3/4((2x/3)+30) + 12 = 84
Ans x = 99
ANSWER:B
Answer: (B) 99
Question: Two numbers A and B are such that the sum of 5% of A and 4% of B is two-third of the sum of 6% of A and 8% of B. Find the ratio of A : B.
(A) 2 : 1
(B) 1 : 2
(C) 4 : 3
(D) 1 : 1
(E) 3 : 2
Rationale: Explanation:
5% of A + 4% of B = 2/3(6% of A + 8% of B)
5A/100 + 4B/100 = 2/3(6A/100+8B/100)
⇒5A + 4B = 2/3(6A + 8B)
⇒15A + 12B = 12A + 16B
⇒ 3A = 4B
⇒ AB = 4/3
⇒ A:B=4:3
Answer: Option C
Answer: (C) 4 : 3
Question: the twonumbers (23__)^32 and (12__)^ 33 has 6 in the last digit what is the missing digit ?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: it should be 6
as last digit in all powers of nos with unit digit 6 is 6.
ANSWER:C
Answer: (C) 6
Question: √184,513 is between
(A) 100 and 200
(B) 200 and 300
(C) 300 and 400
(D) 400 and 500
(E) 500 and 600
Rationale: Look at (A). 200^2 = 40,000 which is much lower than 184,513
Going down the options, you will see that 500^2 = 250,000 which is the first one greater than 184,513.
Hence, answer will be between 400 and 500.
Answer (D)
Answer: (D) 400 and 500
Question: Kamal obtained 76, 60, 72, 65 and 82 marks(out of 100) in English, Mathematics, Physics, Chemistry and Biology. What are his average marks?
(A) 71
(B) 69
(C) 72
(D) 75
(E) NOne
Rationale: Sol.
Average
= 76 + 60 + 72 + 65 + 82 / 5)
= (355 / 5)
= 71.
Answer A
Answer: (A) 71
Question: A man arranges to pay off a debt of Rs 3600 by 40 annual installments which are in A.P. When 30 of the installments are paid he dies leaving one-third of the debt unpaid.
The value of the 8th installment is:
(A) 50
(B) 54
(C) 65
(D) 47
(E) 37
Rationale: Let the first installment be 'a' and the common difference between any two consecutive installments be 'd'
Using the formula for the sum of an A.P :-
S=n/2[2a+(n−1)d].
We have,
3600=40/2[2a+(40-1)d].
3600=20[2a+39d].
180 =2a+39d. ----(i)
Similarly,
2400=30/2[2a+(30-1)d].
160=2a+29d. ----(ii)
On solving both the equations we get:
d=2 and a=51
Hence, the Value of 8th installment is :-
=51+(8−1)2.
=65. Answer : C
Answer: (C) 65
Question: A set of numbers has the property that for any number x in the set, x+6 is also in the set. If -6 is in the set, which of the following must also be in the set
1. 0
2. -12
3. 12
(A) 1 only
(B) 2 only
(C) 1 and 2 only
(D) 1 and 3 only
(E) 1,2 and 3
Rationale: If X is in the set than X+ 6 is also in the set
If -6 in the set than
-6+6= 0 is also in the set
Since + 6 is Present, 6 + 6= 12 Is also present in the set .
Therefore Ans D
Answer: (D) 1 and 3 only
Question: The arithmetic mean of the scores of a group of students in a test was 70. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is?
(A) A)71.4.
(B) B)91.7
(C) C)84.09
(D) D)81.1
(E) E)71.2
Rationale: Let the required means score be x. Then,
20 * 80 + 25 * 31 + 55 * x = 70 * 100
= 1600 + 775 + 55x = 7000
= 55x = 4625
= x = 84.09
Answer:C
Answer: (C) C)84.09
Question: Two fifth of the roads from A to B are at least 5 miles long, and 1/4 of the roads from B to C are at least 5 miles long. If you randomly pick a road from A to B and then randomly pick a road from B to C, what is the probability that at least one of the roads you pick is at least 5 miles long?
(A) 1/6
(B) 11/20
(C) 2/3
(D) 3/4
(E) 11/12
Rationale: So please:
Find the probability of the event thatnoneof the roads you pick will be at least 5 miles long and subtract from 1 to get the probability thatat least oneof the roads you pick will be at least 5 miles long: P=1-3/5*3/4=11/20.
Answer: B.
Answer: (B) 11/20
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
(A) 18.9 sec
(B) 88.9 sec
(C) 22.9 sec
(D) 16.8 sec
(E) 72.0 sec
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec
Answer: D
Answer: (D) 16.8 sec
Question: An article is bought for Rs.600 and sold for Rs.500, find the loss percent?
(A) 16 2/6%
(B) 16 5/3%
(C) 26 2/3%
(D) 16 2/3%
(E) 16 3/3%
Rationale: 600 ---- 100
100 ---- ? => 16 2/3%
Answer: D
Answer: (D) 16 2/3%
Question: To be considered grade AC, an egg must weigh between 75 and 90 grams, including the shell. Shells of grade AC eggs weigh between 3 and 5 grams. What is the smallest possible mass, in grams, of a 12-egg omelet, assuming that only grade AC eggs are used, the shells are all discarded, and no mass is lost in the cooking process?
(A) 800
(B) 840
(C) 864
(D) 900
(E) 1,080
Rationale: We're asked for the smallest possible mass, so what could the lowest mass be per egg AC? A 75 gram egg, with a 5 gram shell, or 70 grams ofcookingmass. 12 x 70 = 840, so the answer is B.
Answer: (B) 840
Question: A bullock-cart travels 24 kilometers in 3 hours and an another bullock-cart travels 120 kilometers in 2 hours. What will be the ratio of their speeds?
(A) 2 : 15
(B) 1 : 5
(C) 2 : 3
(D) 3 : 2
(E) None of these
Rationale: First cart speed will be 24/3=8
Second cart speed is 120/2=60
So, ratio is 8/60=2/15
ANSWER:A
Answer: (A) 2 : 15
Question: we need to carve out 125 identical cubes from a cube . what is the minimum number of cuts needed?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Total no. of cubes=n^3
here n^3 =125 which makes n=5,
also minimum no. of cuts required =3(n-1)
hence, 3(5-1)=12 cuts.
ANSWER:E
Answer: (E) 12
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet ?
(A) 9 a.m
(B) 10 a.m
(C) 10-30 a.m
(D) 11 a.m
(E) None
Rationale: Solution
Distance covered by A in x hours	= 20 x km
Distance covered by B in (x - 1) hours	= 25 (x - 1) km
= 20x + 25 (x - I)
= 110
= 45x = 135
x = 3. So, they meet at 10 a.m
Answer B
Answer: (B) 10 a.m
Question: If x is a positive integer, then the least value of x for which x! is divisible by 10 is?
Can someone please explain intuitively what the question is asking?
(A) 5
(B) 9
(C) 12
(D) 15
(E) 30
Rationale: In order x! to be divisible by 1,0, it should have at least 1 trailing zeros. A trailing 0 in factorial of a number is produced by 2 and 5 in it: 2*5 = 10. So, we need 10 to be in x! at least in power of 1.
5! = 120 has 1 trailing zeros.
Answer: A
Answer: (A) 5
Question: Three interviewers, A, B, and C are interviewing 40 applicants. Only with three interviewers' admission can an applicant be admitted. If interviewer B admitted 15 applicants, A admitted 17 applicants, and C admitted 20 applicants, at least how many applicants get the admission?
(A)  8
(B)  2
(C)  6
(D)  0
(E)  12
Rationale: If B admitted 15 are overlapping with A admission of 17 But C does not overlap with anybody.
Then no student will get nod from all the 3.
Hence 0 student will get admission.
Answer : D
Answer: (D)  0
Question: Simplify: 839478 x 625
(A) 527346750
(B) 524673750
(C) 526473750
(D) 526475730
(E) None of them
Rationale: 839478 x 625 = 839478 x 5^4 = 8394780000/16
= 524673750.
Answer is C.
Answer: (C) 526473750
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line after each of Frederick, Gale, and Harold?
(A) 1,008
(B) 1,296
(C) 1,512
(D) 2,018
(E) 2,016
Rationale: Place D and E first: 8 options for D, 7 options for E.
We are left with 6 empty places. A, B and C must take first 3 places and F, G, H must take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for F, G, and H.
Total = 8*7*3!*3! = 2,016.
Answer: E.
Answer: (E) 2,016
Question: The remainder of the division of a number by 63 is 27. What will be the remainder when that number is divided by 6?
Please explain
(A) 4
(B) 5
(C) 6
(D) 7
(E) 0
Rationale: The easiest way to solve this question is by plugging in a number. Here are the steps I followed:
1) Choose a number X that when divided by 63 gives you 27 as a remainder. So I did x = 63 + 27 = 90. (90/63 = 1R27)
2) Divide that number by 6. 90/5 = 15R0
Since the remainder is 0, the correct answer is choice E.
Answer: (E) 0
Question: Calculate the circumference of a circular field whose radius is 10 centimeters.
(A) 20 π cm
(B) 19 π cm
(C) 28 π cm
(D) 25 π cm
(E) 30 π cm
Rationale: Circumference C is given by
C = 2πr = 2π*10 = 20 π cm
Answer: A
Answer: (A) 20 π cm
Question: I. a2 - 13a + 42 = 0,
II. b2 - 15b + 56 = 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 a ≤ b
(E) If a = b or the relationship between a and b cannot be established.
Rationale: Explanation:
I. a2 - 13a + 42 = 0
=>(a - 6)(a - 7) = 0 => a = 6, 7
II. b2 - 15b + 56 = 0
=>(b - 7)(b - 8) = 0 => b = 7, 8
=>a ≤ b
Option D
Answer: (D) If a ≤ b
Question: What distance will be covered by a bus moving at 90 kmph in 20 seconds?
(A) 500
(B) 600
(C) 289
(D) 276
(E) 207
Rationale: 90 kmph = 90 * 5/18
= 25 mps
D = Speed * time = 25 * 20
= 500 m.
Answer:A
Answer: (A) 500
Question: Youseff lives x blocks from his office. It takes him 1 minute per block to walk to work and 20 seconds per block to ride his bike to work. It is takes him exactly 4 minutes more to walk to work than to ride his bike to work, then x equals?
(A) 4
(B) 6
(C) 10
(D) 15
(E) 20
Rationale: Please follow posting guidelines, link is in my signatures.
As for your question, x/60 = blocks/time/block = block^2/time . This is not what you want. You are given x blocks and 60 seconds PER BLOCK. Thus you need to put it as 60*x to give you units of seconds as you are equating this to 240 (which is TIME in seconds.).
Thus the correct equation is : 60*x-20*x=240----> 40x=240--> x = 6
Option B
Answer: (B) 6
Question: Sum of the squares of 3 no.'s is 179 and the sum of their products taken two at a time is 131. Find the sum?
(A) 20
(B) 21
(C) 26
(D) 28
(E) 30
Rationale: (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 179 + 2* 131
a + b + c = √441 = 21
B
Answer: (B) 21
Question: The dimensions of a room are 25 feet * 15 feet * 12 feet. What is the cost of white washing the four walls of the room at Rs. 4 per square feet if there is one door of dimensions 6 feet * 3 feet and three windows of dimensions 4 feet * 3 feet each?
(A) s.4528
(B) s.3624
(C) s.4527
(D) s.4530
(E) s.4521
Rationale: Area of the four walls = 2h(l + b)
Since there are doors and windows, area of the walls
= 2 * 12 (15 + 25) - (6 * 3) - 3(4 * 3)
= 906 sq.ft.
Total cost = 906 * 4
= Rs.3624
Answer:B
Answer: (B) s.3624
Question: a man can row 24 kmph in still water.it takes him thrice as long to row up as to row down the river.find the rate of stream
(A) 13 km/hr.
(B) 12 km/hr.
(C) 9 km/hr.
(D) 15 km/hr.
(E) 11 km/hr.
Rationale: Let manâ€™s rate upstream be x kmph.then ,his rate downstream=3xkmph.
So,2x=24 or x=12.
Rate upstream=12 km/hr,rate downstream=36 km/hr.
Hence,rate of stream=1/2(36-12)km/hr=12 km/hr.
Answer is B.
Answer: (B) 12 km/hr.