mathewhe/aqua_rat huggingface dataset:
Question: An unbiased die is tossed. Find the probability of getting a multiple of 4
(A) A)1/3
(B) B)2/5
(C) C)1/4
(D) D)1/6
(E) E)3/7
Rationale: Here S = {1,2,3,4,5,6}
E = event of getting a multiple of 4
E = {4}
P(E) = 1/6
Answer is D
Answer: (D) D)1/6
Question: A number of 53 marbles is to be divided and contain with boxes. If each box is to contain 3, 4, or 5 marbles, what is the largest possible number of boxes?
(A) 10
(B) 12
(C) 15
(D) 16
(E) 17
Rationale: To maximize # of boxes we should minimize marbles per box: 16*3+1*5=53 --> 16+1=17.
Answer: E.
Answer: (E) 17
Question: The hen lays 3 eggs then she lays 6 eggs more. Totally how many eggs she lays?
(A) 3
(B) 9
(C) 19
(D) 11
(E) 23
Rationale: 3+6=9. Answer is B.
Answer: (B) 9
Question: The operation T is defined by x T y=1/x+1/y for all nonzero numbers x and y. If z is a number greater than 1, which of the following must be true.
I. x T (-z)=0
II. 2/z T 2/z=z
III. z T z/z-1=1
(A) a.) I
(B) b.) I and II only
(C) c) I and III only
(D) d) II and III only
(E) e) I, II and III only
Rationale: Statement I is TRUE
Statement II is TRUE
Statement III is not TRUE
Answer : B
Answer: (B) b.) I and II only
Question: N is an even 3-digit number such that the last 3 digits of N^2 are N itself. What is the value of N?
(A) 141376
(B) 241376
(C) 141476
(D) 181376
(E) 141396
Rationale: 376*376=141376
ANSWER:A
Answer: (A) 141376
Question: A 12% stock yielding 10% is quoted at :
(A) 83.33
(B) 110
(C) 112
(D) 120
(E) 160
Rationale: Solution
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 12, money invested = Rs.(100/10X12) = Rs. 120.
∴ Market value of Rs. 100 stock =Rs. 120
Answer D
Answer: (D) 120
Question: Sheik Abdullah decides to buy 2 new cars for his collection. If he has to choose between nine different cars, what is the number of purchasing possibilities he has?
(A) A)1312
(B) B)1412
(C) C)1512
(D) D)1612
(E) E)1712
Rationale: Sheik Abdullah decides to buy 2 new cars for his collection. He has to choose between nine different cars
8C3= 9*8*7*6/(2*1) = 1512 ANS:C
Answer: (C) C)1512
Question: At a certain school, the ratio of the number of English majors to the number of Sociology majors is 5 to 2, and the ratio of the number of Psychology majors to the number of Sociology majors is 3 to 4. If the ratio of the number of History majors to the number of English majors is 5 to 3, what is the ratio of the number of Psychology majors to the number of History majors
(A) 25 to 3
(B) 10 to 9
(C) 9 to 50
(D) 6 to 25
(E) 3 to 10
Rationale: Correct
A
Answer: (A) 25 to 3
Question: If p = ||q – 3| – 2|, for how many values of q is m = 6?
(A) 5
(B) 4
(C) 3
(D) 2
(E) 1
Rationale: p = ||q – 3| – 2| can be 4 only and only when q-3= +/-8. so there are 2 values of q
Answer : D
Answer: (D) 2
Question: x% of y is y% of ?
(A) x
(B) 100x
(C) x/100
(D) y/100
(E) None
Rationale: Answer
Let x% of y = y% of A, then
⇒ xy / 100 = yA/100
∴ A = (xy/100) x (100/y) = x
Correct Option: A
Answer: (A) x
Question: How many odd three-digit integers greater than 400 are there such that all their digits are different?
(A) 140
(B) 156
(C) 172
(D) 181
(E) 200
Rationale: 5 (hundred's digit) * 9 (ten's digit) * 8 (unit's digit) = 360
Now take numbers in the range 400 - 900.
Total numbers where all digits are different = 360 (as before)
[highlight]Number of odd numbers = 5 * 8 * 5 = 200[/highlight] (now there are 5 possibilities for the unit's digit)
E
Answer: (E) 200
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 8 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
A. 40
(A) 87
(B) 8
(C) 46
(D) 44
(E) 64
Rationale: Explanation:
Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 8)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 8 = 4/9(T - 8)
10T = 792 - 352 => T = 44.
Answer: Option D
Answer: (D) 44
Question: If (n+2)!/n!=110, n=?
(A) 2/131
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: (n+2)!/n!= 110
Rewrite as:[(n+2)(n+1)(n)(n-1)(n-2)....(3)(2)(1)]/[(n)(n-1)(n-2)....(3)(2)(1)]= 132
Cancel out terms: (n+2)(n+1) = 110
From here, we might just TEST the answer choices.
Since (11)(10) = 110, we can see that n = 9
B
Answer: (B) 9
Question: g is a negative number and h is a positive number, which of the following options must be positive?
(A) 2g/h
(B) h/g
(C) (a + b)^4
(D) g/h
(E) gh
Rationale: A. 2g/h
-ve/+ve=-ve
B.h/g
-ve/+ve=-ve
C.(a + b)^2
will be positive irrespective of the absolute values of x and y
will be positive always
D.g/h
-ve/+ve=-ve
B.gh
-ve*+ve=-ve
Correct answer C
Answer: (C) (a + b)^4
Question: In a right angled triangle, two sides are consecutive whole number in which one side is hypotenuse. what could be the possible length of third side?
(A) 277
(B) 361
(C) 269
(D) 171
(E) 112
Rationale: Explanation:
Pythagorean triplets are generated with each "odd number" greater than 1 by using a formula.
If n is an odd number, then Pythagorean triplet = n,n2−12,n2+12n,n2−12,n2+12.
Here 361 is an odd number. So the triplet is 361, 65160, 65161.
Answer:B
Answer: (B) 361
Question: In 1990 a total of p earthquakes occurred worldwide, some but not all of which occurred in Asia. If r of these earthquakes occurred in Asia, which of the following represents the ratio of the number of earthquakes that occurred in Asia to the number that did NOT occur in Asia?
(A) p/r
(B) r/p
(C) r/(p-r)
(D) p/(p-r)
(E) 1- (r/p)
Rationale: We're given a couple of facts to work with:
1) There were a total of p earthquakes
2) Of those earthquakes, r of them occurred in Asia
We're asked for the ratio of the number of earthquakes that occurred IN ASIA to the number of earthquakes that DID NOT occur in Asia.
Let's TEST VALUES
p = 5 total earthquakes
r = 2 occurred in Asia
Thus, there were 3 earthquakes that DID NOT occur in Asia....
The answer to the question is 2:3
We just need to plug in the values for p and r and find the match...
Answer A: p/r = 5/2 NOT a match
Answer B: r/p = 2/5 NOT a match
Answer C: r/(p-r) = 2/(5-2) = 2/3 This IS a match
Answer D: p/(p-r) = 5/(5-2) = 5/3 NOT a match
Answer E: 1 - (r/p) = 1-2/5 = 3/5 NOT a match
C
Answer: (C) r/(p-r)
Question: The length of a rectangle is double its width. If the length is diminished by 5cm and the width is increased by 5cm then its area is increased by 75cm square. What is the length of the rectangle?
(A) 20
(B) 30
(C) 40
(D) 56
(E) 65
Rationale: Sol. According to question
(l-5)(b+5)-lb = 75
And l = 2b
So, b = 20, l = 40
Ans.(C)
Answer: (C) 40
Question: The two roots of the quadratic equation x2 - 85x + c = 0 are prime numbers. What is the
value of c?
(A) 84
(B) 166
(C) 332
(D) 664
(E) 1328
Rationale: Assuming that two prime numbers x1 and x2 are the solutions, then x1 + x2 = 85.
Since 85 is an odd number, either x1 or x2 must be an even number. The only even prime
number is 2. Therefore, one number must be 2 and the other 83. Hence c = 2 *83 = 166.
correct answer B
Answer: (B) 166
Question: A person was asked to state his age in years. His reply was, "Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will know how old I am." What was the age of the person?
(A) 18
(B) 19
(C) 71
(D) 16
(E) 17
Rationale: Let the present age of the person be x years.
Then, 3(x + 3) - 3(x - 3) = x
3x + 9 - 3x + 9 = x => x = 18
Answer:A
Answer: (A) 18
Question: A credit union customer borrowed $15,000, but received y dollars less than this due to discounting. If there was a separate $20 service charge, then, in terms of y, the service charge was what fraction of the amount that the customer received?
(A) 20/(15,000 + y)
(B) 25/(10,000 - y)
(C) 20/(15,000 - y)
(D) 20y/(15,000 - y)
(E) 20(y-1)
Rationale: The amount of money the customer received was (15,000 - y) dollars. The $20 service charge as a fraction of the amount received was, therefore, 20/(15,000 - y).
Answer: A.
Answer: (A) 20/(15,000 + y)
Question: If a cards are drawn from apack of 82 cards. The probability of getting a queen of club or a king of heart is
(A) 1/31
(B) 1/24
(C) 1/31
(D) 1/45
(E) 1/41
Rationale: Here, n(S) = 52.
Let E = event of getting a queen of club or a king of heart.
Then, n(E) = 2.
P(E) =	n(E)	=	2/82	=	1/41	.
n(S)
E
Answer: (E) 1/41
Question: 5 years ago Kate was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find the age of son?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: let x be the mother's age and y be the son's age
x-5=5(y-5)
x+5=3(y+5)-8
by solving this we get x=35 and y=11
ANSWER:E
Answer: (E) 11
Question: If the selling price of 50 articles is equal to the cost price of 30 articles, then the loss or gain percent is:
(A) 10%
(B) 40%
(C) 30%
(D) 25%
(E) 35%
Rationale: Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 30.
Loss % = 20/50 * 100 = 40%
ANSWER:B
Answer: (B) 40%
Question: P alone can complete a job in 12 days. The work done by Q alone in one day is equal to one-half of the work done by P alone in one day. In how many days can the work be completed if P and Q work together?
(A) 5
(B) 6
(C) 7
(D) 8
(E) 9
Rationale: P's rate is 1/12
Q's rate is 1/24
The combined rate is 1/12 + 1/24 = 1/8
If they work together, the job will take 8 days.
The answer is D.
Answer: (D) 8
Question: Jane makes toy bears. When she works with an assistant, she makes 70 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: We can use fractional equivalents here to solve the problem
80% = 4/5; this means that in 1st case if she prepares 5 bears, in 2nd case she prepares 9 bears
10% = 1/10; this means that in 1st case if she needs 10 hours, in 2nd case she needs 9 hours
Now we come to productivity
Based on above fractional values the productivity in 1st case is 0.5 bears / hour and in the 2nd case it is 1 bear / hour
Hence the productivity is double with the assistant i.e. the increase in productivity is 80%
B
Answer: (B) 80%
Question: Maya purchase 15 jars in a store then she returned 5 jars to store .Now how many jars she had?
(A) A)5
(B) B)11
(C) C)19
(D) D)10
(E) E)4
Rationale: 15-5=10. Answer is D
Answer: (D) D)10
Question: The principal that amounts to Rs. 4893 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
(A) s. 3096
(B) s. 4076
(C) s. 4085
(D) s. 4096
(E) s. 5096
Rationale: Principal = [4913 / (1 + 25/(4 * 100))3]
= 4893 * 16/17 * 16/17 * 16/17 = Rs. 4085.
ANSWER:C
Answer: (C) s. 4085
Question: Look at this series: 15, 15, 27, 27, 39, 39, 51, 51, ... What number should fill the blank?
(A) 51
(B) 39
(C) 63
(D) 15
(E) None
Rationale: Explanation: In this simple addition with repetition series, each number in the series repeats itself, and then increases by 12 to arrive at the next number.
Answer: Option C
Answer: (C) 63
Question: Increasing the original price of an article by 6 percent and then increasing the new price by 6 percent is equivalent to increasing the original price by
(A) 12.1%
(B) 12.36%
(C) 12.94%
(D) 13.65%
(E) 14.56%
Rationale: 1.06*1.06*x = 1.1236*x
The answer is B.
Answer: (B) 12.36%
Question: A and B together can do a work in 7 days. If A alone can do it in 56 days. In how many days can B alone do it?
(A) 11
(B) 8
(C) 21
(D) 20
(E) 25
Rationale: B
8
1/7 â€“ 1/56 = 1/8 => 8
Answer: (B) 8
Question: Pipes A and B can fill a cistern in 8 and 56 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
(A) 13
(B) 14
(C) 16
(D) 18
(E) 19
Rationale: :
1/8 + 1/56 = 1/7
7 * 2 = 14.Answer:B
Answer: (B) 14
Question: A coin is tossed 4 times. What is the probability that the number of Heads is equal to the number of Tails?
(A) 1/8
(B) 1/4
(C) 3/8
(D) 1/2
(E) 9/16
Rationale: We have to find the probability that we get 2 heads and 2 tails in 4 tosses of the coin.
Using the binary formula and defining a head as a success,
P(2 heads in 4 tosses) = 4C2* (1/2)^2 * (1/2)^2
= 6/16
= 3/8
The answer is therefore (C)
Answer: (C) 3/8
Question: The salary of all officers is increased twice successively by 20%. What is the net percentage increase in their salaries?
(A) 20%
(B) 40%
(C) 21%
(D) 44%
(E) 48%
Rationale: M . F = 120/100*120/100 = 36/25
Net % increase = ( M . F -1 ) *100 =( 36/25-1) * 100
11/25 *100 = 44 %
ANSWER:D
Answer: (D) 44%
Question: A sum of money invested at C.I. amounts to Rs. 800 in 3 years to Rs. 860 in 4 years. The rate of interest per annum is?
(A) 2 1/2 %
(B) 4%
(C) 5%
(D) 6 2/3 %
(E) 7 1/2%
Rationale: S.I. on Rs. 800 for 1 year = (860 - 800) = Rs. 60 Rate = (100 * 60)/(800 * 1) = 7 1/2%
ANSWER:E
Answer: (E) 7 1/2%
Question: If (y - 1)(z - 9) +15(z - 9) = 0, then which of the following must be true?
(A)  y = -4 and z = -3
(B)  y = -4 or z = -3
(C)  y = -4 or z = 9
(D)  y = 1 and z = 3
(E)  y = 1 or z = 3
Rationale: factor out:
(z-9)(y-1+15)=0
(z-9) (y+14) = 0
So by checking options we get ,
C.
Answer: (C)  y = -4 or z = 9
Question: The area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is?
(A) 0.35 cm2
(B) 17.5 cm2
(C) 8.75 cm2
(D) 55 cm2
(E) 65 cm2
Rationale: Explanation:
(5 * 3.5)/2 = 8.75
ANSWER IS C
Answer: (C) 8.75 cm2
Question: The angle between the minute hand and the hour hand of a clock when the time is 8.30, is:
(A) 75
(B) 60
(C) 35
(D) 45
(E) 50
Rationale: hr hand in 17/2 hrs = (360/12 * 17/2) =255
hr hand in 30 min = (360/60 * 30) = 180
req angle = (255-180) = 75d
ANSWER A
Answer: (A) 75
Question: A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 12375. What is the share of C?
(A) Rs. 2250
(B) Rs. 3375
(C) Rs. 6750
(D) Rs. 5625
(E) None of these
Rationale: Explanation:
Let the investment of C be Rs. x.
The inverstment of B = Rs.(2x/3)
The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)
Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3
C's share = Rs. [(3/11) × 12375] = Rs. 3375
Answer: Option B
Answer: (B) Rs. 3375
Question: Ages of two coworkers differ by 26 years. If 8 years ago, the elder one was twice as old the younger one, find their present age
(A) 12,38
(B) 14,40
(C) 16,42
(D) 28,54
(E) 34,60
Rationale: Explanation:
Let the age of younger person is x,
Then elder person's age is (x+26)
=> 2(x-8) = (x+26-8) [8 years before]
=> 2x-16 = x+18
=> x = 34.
So elder person's age is x + 26 = 60
Answer: Option E
Answer: (E) 34,60
Question: The radius of a semi circle is 6.8 cm then its perimeter is?
(A) 32.7
(B) 32.4
(C) 22.4
(D) 34.9
(E) 35.1
Rationale: 36/7 r = 6.8 = 34.9
Answer:D
Answer: (D) 34.9
Question: A train covers a distance of 11 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) m
(B) m
(C) m
(D) m
(E) m
Rationale: Speed = (11/10 * 60) km/hr
= (66 * 5/18) m/sec = 55/3 m/sec.
Length of the train = 55/3 * 6
= 110 m.
Answer:C
Answer: (C) m
Question: In a 1000 m race, A beats B by 90 m and B beats C by 100 m. In the same race, by how many meters does A beat C?
(A) 145 m
(B) 176 m
(C) 181 m
(D) 159 m
(E) 218 m
Rationale: By the time A covers 1000 m, B covers (1000 - 90) = 910 m.
By the time B covers 1000 m, C covers (1000 - 100) = 900 m.
So, the ratio of speeds of A and C =
1000/910 * 1000/900 = 1000/819 So, by the time A covers 1000 m, C covers 819 m.
So in 1000 m race A beats C by 1000 - 819 = 181 m.
Answer:C
Answer: (C) 181 m
Question: A train 210 m long passed a pole in 21 sec. How long will it take to pass a platform 310 m long?
(A) 19
(B) 32
(C) 52
(D) 74
(E) 83
Rationale: Speed = 210/21 = 10 m/sec.
Required time = (210 + 310)/10 = 52 sec.
Answer: C
Answer: (C) 52
Question: If x2 + kx - 3, is divisible by (x - 1), What is the value of k
(A) -1
(B) 1
(C) 2
(D) -1
(E) 0
Rationale: Explanation:
If x2 + kx - 3 is divisible by (x - 1) then x = 1
(1)2 + 1(k) - 3 = 0
1 + k - 3 = 0
k = 2
Answer: Option C
Answer: (C) 2
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 49 hours respectively. The ratio of their speeds is?
(A) 4:5
(B) 7:3
(C) 4:4
(D) 7:8
(E) 7:1
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √49 : √9
= 7:3
Answer: B
Answer: (B) 7:3
Question: What are the last three number of this series 11234783131?
(A) 191
(B) 192
(C) 193
(D) 194
(E) 195
Rationale: 23-11= 12
47-23=24
83-47=36
131-83=48
Thus all differences are multiple of 8.
so, 131+60=191
ANSWER:A
Answer: (A) 191
Question: A mom and dad want to take thier 16 year old daughter, 14 year old son and 7 year old son on a trip to Six Flags. An adult ticket costs $25.50. A child under the age if 12 costs $20.50 and children under 5 are free. There is a promotion to get 15% off of two adult tickets when you buy two adult tickets at full price. How much will it cost the family total including the discount to purchase their tickets?
(A) 122.5
(B) 43.35
(C) 114.85
(D) 107.2
(E) 94.35
Rationale: 25.50*2= Y = 51.
Y*.15=7.65
Y-7.65=X = 43.35
Y= price of two adult tickets
X= price of two adult tickets after the discount
X+Y+20.50=114.85
The answer is C.
Answer: (C) 114.85
Question: If a certain sample of data has a mean of 18.0 and the value 26.0 is more than 2.5 standard deviations from the mean, which of the following could be the standard deviation of the sample
(A) 3.75
(B) 3.5
(C) 3.15
(D) 3.85
(E) 2.75
Rationale: 26.0 is more than 2.5 standard deviations from 18 --> 26 > 18 + 2.5*{SD} --> 2.5*{SD} < 8 --> {SD} < 3.2. Only option C offers the standard deviation less than 3.2.
Answer:C
Answer: (C) 3.15
Question: A man saves Rs 100 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years.
(A) Rs 331.01
(B) Rs 362.01
(C) Rs 362.02
(D) Rs 362.03
(E) None of these
Rationale: Explanation:
=[100(21/20Ã—21/20Ã—21/20)+100(21/20Ã—21/20)+100(21/20)]=662.02
Option A
Answer: (A) Rs 331.01
Question: In how much time will a train of length 100 m, moving at 36 kmph cross an electric pole?
(A) 15 sec
(B) 12 sec
(C) 10 sec
(D) 14 sec
(E) 11 sec
Rationale: C
10 sec
Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 100/10 = 10 sec.
Answer: (C) 10 sec
Question: 6persons enter a lift on the ground floor of a 9floor apartment. Assuming that each of them independently & with equal probability can leave the lift at any floor beginning with the first, what is the probability that all the 6persons are leaving the lift at different floors?
(A) 5P6/8^3
(B) 7P6/8^2
(C) 8P6/8^6
(D) 9P6/8^5
(E) 9P6/8^4
Rationale: Apart from the ground floor, there are 8 floors
Let's find out the total number of ways in which all the six persons can leave the
lift at eight different floors
The 1st person can leave the lift in any of the 8 floors (8 ways)
The 2nd person can leave the lift in any of the remaining 7 floors (7 ways)
The 3nd person can leave the lift in any of the remaining 6 floors (6 ways)
...
The 6th person can leave the lift in any of the remaining 3 floors (3 ways)
Total number of ways = 8 × 7 × 6 × 5 × 4 × 3 = 8P6
(In fact, from the definition of permutations itself,
we will be able to directly say that the number of ways in which all the six persons
can leave the lift at 8 different floors = 8P6)
n(E)= Total Number of ways in which all the six persons can leave the lift at eight
different floors = 8P6
Now we will find out the total number of ways in which each of the six persons
can leave the lift at any of the eight floors
The 1st person can leave the lift in any of the 8 floors (8 ways)
The 2nd person can leave the lift in any of the 8 floors (8 ways)
The 3nd person can leave the lift in any of the 8 floors (8 ways)
...
The 6th person can leave the lift in any of the 8 floors (8 ways)
Total number of ways = 8 × 8 × 8 × 8 × 8 × 8 = 86
i.e., The total number of ways in which each the six persons can leave the lift
at any of the eight floors = n(S) = 86
P(E) = n(E)n(S)=8P6/8^6
C
Answer: (C) 8P6/8^6
Question: By selling 12 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%?
(A) 9
(B) 4
(C) 8
(D) 7
(E) 65
Rationale: 80% --- 12
120% --- ?
80/120 * 12 = 8
Answer: A
Answer: (A) 9
Question: Donovan took a math test and got 35 correct and 11 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
(A) 57.78%
(B) 67.78%
(C) 76.09%
(D) 47.78%
(E) 97.78%
Rationale: 35 correct our of 46 total (35+11)
35/46
correct answer C
Answer: (C) 76.09%
Question: What distance (in meters) will be covered by a bus moving at 54 km/hr in 15 seconds?
(A) 175
(B) 200
(C) 225
(D) 250
(E) 275
Rationale: 54 km/hr = 54 * 5/18 = 15 m/s
distance = 15 * 15 = 225 meters
The answer is C.
Answer: (C) 225
Question: Based on this year's costs, an orcharde grower budgets P dollars for planing N new trees next year. If the average cost of planting each tree were to increase 50% from this year's cost, then the greatest number of trees that the orchard grower could plant next year using P dollars would be
(A) 33% less than N
(B) 25% less than N
(C) equal to N
(D) 20% greater than N
(E) 25% greater than
Rationale: Correct answer is (A).
This year, the price of a tree is price1=P/N.
If this price increases by 50% it becomes price2=P/N*1.50
Then with P dollars, you can grow P/price2 tress i.e. P/(P/N*1.50) i.e. N/1.5 i.e. .67% less*
A
Answer: (A) 33% less than N
Question: Out of three consecutive odd numbers nine times the first number is equal to addition of twice the third number and adding 9 to twice the second . What is the first number?
(A) 20/21
(B) 23/25
(C) 24/23
(D) 22/5
(E) 21/5
Rationale: Description :
=> 9x=2(x+2)+9+2(x+4)
=> 9x=4x+21
=> 5x=21
x=21/5
Answer E
Answer: (E) 21/5
Question: How many integers between 50 and 200 are there such that their unit digit is even?
(A) 50
(B) 75
(C) 100
(D) 150
(E) 200
Rationale: 150 numbers between 50 and 200
Out of which half would be even, half would be odd.
Number of even unit digit number = 75.
The correct option is B
Answer: (B) 75
Question: An electric pump can fill a tank in 5 hours. Because of a leak in the tank, it took 10hours to fill the tank. If the tank is full, how much time will the leak take to empty it?
(A) 10hours
(B) 12hours
(C) 8hours
(D) 5hours
(E) 15hours
Rationale: Work done by the leak in 1 hour = 1/5 - 1/10 = 1/10
The leak will empty the tank in 10hours
Answer is A
Answer: (A) 10hours
Question: Let the second number be 3x, so that the first number is 6x and the third number is 2x.
(A) 22
(B) 77
(C) 98
(D) 27
(E) 36
Rationale: ∴ 6x + 3x + 2x = 132 ⇒ x = 12. Second number = 3x = 3×12 = 36.
Answer:E
Answer: (E) 36
Question: In a garden, trees are planted in rows. In each row there are as many trees as the number of rows in the garden. If each tree bears as many fruits as the number of trees in each row and if the total number of fruits from the trees in that garden is n, then :
(A) n is a perfect square
(B) n is an odd number
(C) n is an even number
(D) n is a perfect cube.
(E) none
Rationale: say for example, there are 4 rows in d garden, then there will b 4 trees in each row and each tree wud bear 4 fruits..Then total no of fruits in d garden wud b (4*4)*4= 64...which is a cube of 4.
ANSWER:D
Answer: (D) n is a perfect cube.
Question: There are 3 pairs of socks and 2 socks are worn from that such that the pair of socks worn are not of the same pair. what is the number of pair that can be formed.
(A) 5
(B) 1
(C) 3
(D) 6
(E) 7
Rationale: First of all you should remember that there is a difference in left and right sock.
now no. of way to select any of the sock = 3
and for second = 2
so total methods = 3*2 = 6
ANSWER:D
Answer: (D) 6