mathewhe/aqua_rat huggingface dataset:
Question: If a and b are digits, and the number a99,99b/88 = an integer, what are the values of a and b?
(A) a = b = 7
(B) a = b = 6
(C) a = b = 3
(D) a = b = 1
(E) a = b = 2
Rationale: a99,99b, divisible by 88.
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
99b/8 => 992/8 = 124 => b = 2
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible by 11.
a9999-2 => a999-7 => a99-2 => a9-7 => a2 => 22/11 = 2.
So a = 2.
Answer: E
Answer: (E) a = b = 2
Question: Two cubes of tire sides ratio 2 : 3. Find its cube volumes ratio?
(A) 2:27
(B) 3:27
(C) 1:27
(D) 8:27
(E) 5:27
Rationale: a(power3) : b(power3) = 2(power3) : 3(power3)
= 8 : 27
Answer is D.
Answer: (D) 8:27
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
(A) 250
(B) 882
(C) 772
(D) 512
(E) 211
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer: A
Answer: (A) 250
Question: An equilateral triangle T2 is formed by joining the mid points of the sides of another equilateral triangle T1. A third equilateral triangle T3 is formed by joining the mid-points of T2 and this process is continued indefinitely. If each side of T1 is 50 cm, find the sum of the perimeters of all the triangles.
(A) 180 cm
(B) 220 cm
(C) 240 cm
(D) 270 cm
(E) 300 cm
Rationale: We have 50 for first triangle, when we join mid-points of first triangle we get the second equilateral triangle then the length of second one is 25 and continues.
So we have 50,25,12.5,...
We have ratio = 1/2, and it is GP type.
Sum of infinite triangle is a/1-r = 50/1-(1/2) = 100
Equilateral triangle perimeter is 3a = 3*100 = 300.
So option E.
Answer: (E) 300 cm
Question: How many numbers between 11 and 90 are divisible by 7 ?
(A) 23
(B) 11
(C) 22
(D) 32
(E) 15
Rationale: The required numbers are 14, 21, 28, 35, .... 77, 84.
This is an A.P. with a = 14 and d = (21 - 14) = 7.
Let it contain n terms.
Then, Tn = 84 => a + (n - 1) d = 84
=> 14 + (n - 1) x 7 = 84 or n = 11.
Required number of terms = 11
ANSWER B 11
Answer: (B) 11
Question: How many integer values Y are there for x such that 1 < 3x + 5 < 17?
(A) Two
(B) Three
(C) Four
(D) Five
(E) Six
Rationale: 1 < 3x + 5 < 17
=> -4 < 3x < 12
=> -4/3 < x < 4
x can take integer values Y -1,0 , 1 , 2 , 3
Answer D
Answer: (D) Five
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
(A) 60%
(B) 23%
(C) 30%
(D) 56%
(E) 73%
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer: C
Answer: (C) 30%
Question: The average of five numbers id 27. If one number is excluded, the average becomes 22. What is the excluded number?
(A) 30
(B) 40
(C) 32.5
(D) 35
(E) 47
Rationale: Explanation:
Sum of 5 numbers = 5 × 27
Sum of 4 numbers after excluding one number = 4 × 22
Excluded number
= 5 × 27 - 4 × 22
= 135 - 88 = 47
Answer: Option E
Answer: (E) 47
Question: Which of the following points falls outside of the region defined by 2y≤6x−8?
(A) (5, 1)
(B) (3, -8)
(C) (1, 0)
(D) (2, 0)
(E) (0, -14)
Rationale: Equation given is 2y<=6x-8
Simplifying this; y<=3x-4
Plug in the values provided in the options,
A. 1<=11
B. -8<=3
C. 0<=-1
D.0<=0
E. -14<=-12
Option C is the answer.
Answer: (C) (1, 0)
Question: A farmer has enough food to feed her 1000 cows for 50 days. After 10 days some of the cows run away and the food was now enough for the same period of 50 days as before. How many cows ran away?
(A) 300
(B) 200
(C) 500
(D) 400
(E) 250
Rationale: 1000 ---- 50
1000 ---- 40
x ---- 50
x*50 = 1000*40
x = 800
1000
-------
200
Answer = B
Answer: (B) 200
Question: Find the L.C.M of 15, 18, 28 and 30.
(A) 1800
(B) 1260
(C) 1460
(D) 1600
(E) 960
Rationale: Explanation:
2 x 3 x 5 x 3 x 14 = 1260
Answer: Option B
Answer: (B) 1260
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 36 years now, the son's age five years back was:
(A) 13
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: Let the son's present age be x years. Then, (36 - x) = x
2x = 36.
x = 18.
Son's age 5 years back (18 - 5) = 13 years.
Answer: Option A
Answer: (A) 13
Question: A train 310 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
(A) 40
(B) 56
(C) 41
(D) 36
(E) 34
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 310 + 140 = 450 m
Required time = 450 * 2/25 = 36 sec
Answer: Option D
Answer: (D) 36
Question: A sum fetched a total simple interest of $4241.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
(A) $8829
(B) $2840
(C) $6578
(D) $7782
(E) $8930
Rationale: E
8930
Principal
= $100 x 4241.25/9 x 5
= $424125/45
= $8930.
Answer: (E) $8930
Question: 9 3/4 + 8 2/17 - 9 1/15=?
(A) 7 719/1020
(B) 9 817/1020
(C) 9 719/1020
(D) 8 817/1020
(E) None of them
Rationale: Given sum=9+3/4+8+2/17-(9+1/15)
=(9+8-9)+(3/4+2/17-1/15)
=8+(765+120-68/1020
=8 817/1020
Answer is D
Answer: (D) 8 817/1020
Question: There are 10 players in a chess group, and each player plays each of the others once. Given that each game is played by two players, how many total games will be played?
(A) 10
(B) 30
(C) 45
(D) 60
(E) 90
Rationale: 10 players are there.
two players play one game with one another.
so 10C2=10*9/2
=45
SO OPTION C is correct
Answer: (C) 45
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
(A) 14
(B) 66
(C) 88
(D) 99
(E) 12
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.Answer:A
Answer: (A) 14
Question: The ratio of 5 seconds to 4 hours
(A) 1:80
(B) 1:6000
(C) 1:3600
(D) 1:400
(E) 1:500
Rationale: 1 hour =3600 sec
then 5 hours =5*3600=18000
so ,5:18000=1:3600
ANSWER:C
Answer: (C) 1:3600
Question: The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the numbers is 480, then the other is:
(A) 11
(B) 10
(C) 8
(D) 15
(E) 12
Rationale: Other number =	(12 x 600)/480 = 15.
ANSWER :D
Answer: (D) 15
Question: Lake A has a duck population of 36 females and 30 males. Lake B’s duck population consists of the same ratio of females to males. If 6 new female ducks are added to Lake B and no other ducks are added or removed, the new total duck population of Lake B could be which of the following?
(A) 144
(B) 105
(C) 78
(D) 51
(E) 77
Rationale: Lake A has a duck population of 36 females and 35 males --> the ratio is F:M = 36:30 = 6:5.
Lake B’s duck population consists of the same ratio of females to males --> F:M = 6:5.
E
Answer: (E) 77
Question: The number of ways in which six boys and six girls can be seated in a row for a photograph so that no two girls sit together is?
(A) 7! * ⁷P₆
(B) 6! * ⁷P₆
(C) 8! * ⁷P₆
(D) 2! * ⁷P₆
(E) 5! * ⁷P₆
Rationale: We can initially arrange the six boys in 6! ways.
Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.
Hence required number of ways
= 6! * ⁷P₆
Answer: B
Answer: (B) 6! * ⁷P₆
Question: The instructions state that Cheryl needs 3/8 square yards of one type of material and 1/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 15/40 square yards left that she did not use. What is the total amount of square yards of material Cheryl used?
(A) 1/12
(B) 1/9
(C) 2/3
(D) 1/3
(E) 2 1/9
Rationale: total bought = 3/8+1/3
left part 15/40--->3/8
so used part 3/8+1/3-3/8=1/3
Ans D
Answer: (D) 1/3
Question: In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of that of his mother. The wife is 9 years younger to her husband and the brother is seven years older than his sister. What is the age of the mother ?
(A) 40 years
(B) 45 years
(C) 50 years
(D) 60 years
(E) 70 years
Rationale: let daughter age x then father age will be 3x
let mother age is y then son age will be y/2
accor. to que.
3x-y=9 ....................1
y/2-x=7 =>2x-y = -14......2
solve the both eqe.
y=60
ANSWER:D
Answer: (D) 60 years
Question: Two pipes P and Q can fill a cistern in 12 and 15 minutes respectively. Both are opened together, but at the end of 4 minutes the first is turned off. How much longer will the cistern take to fill?
(A) 10 1/7
(B) 10 1/4
(C) 10 1/3
(D) 10 1/2
(E) 10
Rationale: 4/12 + x/15 = 1
x= 10.Answer: E
Answer: (E) 10
Question: In how many different number of ways 3 men and 2 women can sit on a shopa which can accommodate persons?
(A) 170
(B) 180
(C) 200
(D) 5
(E) 220
Rationale: Option 'D'
5p1 = 5 = 5
Answer: (D) 5
Question: Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 153 per Kg , the price of the third variety per Kg will be?
(A) Rs. 147.50
(B) Rs. 785.50
(C) Rs. 175.50
(D) Rs. 258.50
(E) None of these
Rationale: Explanation :
Since first and second varieties are mixed in equal proportions.
So, their average price =Rs. (126+135)/2.
=>Rs. 130.50.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.
We have to find x.
By the rule of alligation, we have:
Cost of 1 kg Cost of 1 kg
of 1st kind of 2nd kind
(Rs. 130.50) (Rs. x)
\ /
Mean Price
(Rs. 153)
/ \
x−153 22.50
=>x−(153/22.50)=1.
=>x−153=22.50.
=>x= 175.50 Rs.
Answer : C
Answer: (C) Rs. 175.50
Question: A train overtakes two persons walking along a railway track. The first one walks at 4.5 km/hr. The other one walks at 5.4 km/hr. The train needs 8.4 and 8.5 seconds respectively to overtake them. What is the speed of the train if both the persons are walking in the same direction as the train?
(A) 81
(B) 66
(C) 55
(D) 42
(E) 30
Rationale: 4.5 km /hr = (4.5*5/18) = 5/4 m/sec = 1.25 m/sec
5.4 km/hr = (5.4*5/18) = 3/2 = 1.5 m/sec
speed = (x-1.25)*8.4=(x-1.5)*8.5
x=22.5
speed = 22.5*18/5 = 81 km/hr
ANSWER A
Answer: (A) 81
Question: A certain quantity of 55% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
(A) 1:3
(B) 1:2
(C) 2:3
(D) 2:1
(E) 3:1
Rationale: 25% - - - - - - - - - 35% - - - - - - 55%
From 25 to 35 =10
From 35 to 55 = 20
So the ratio is 10/20 = 1 to 2
D it is
Answer: (D) 2:1
Question: Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence?
(A) 26/37
(B) 26/35
(C) 26/39
(D) 26/33
(E) 26/31
Rationale: Let ages of Ramu and Shyam be x and y respectively.
x/y = 3/4 => x = 3/4 y
(x- 7)/(y - 7) = 2/3
=> 3x - 21 = 2y - 14 => 3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28years
=> x = 21 years
Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.
Answer:D
Answer: (D) 26/33
Question: The average of 1st 3 of 4 numbers is 7 and of the last 3 are 5. If the sum of the first and the last number is 13. What is the last numbers?
(A) 4
(B) 5
(C) 3.5
(D) 7
(E) 8
Rationale: A + B + C = 21
B + C + D = 15
A + D = 13
A – D = 6
A + D = 13
2D = 7
D = 3.5
ANSWER:C
Answer: (C) 3.5
Question: Four staff members at a certain company worked on a project. The amounts of time that the four staff members worked on the project were in the ratio 2 to 3 to 5 to 6. If one of the four staff members worked on the project for 60 hours, which of the following CANNOT be the total number of hours that the four staff members worked on the project?
(A) 480
(B) 96
(C) 160
(D) 192
(E) 320
Rationale: A:B:C:D=2x:3x:5x:6x, for some positive number x. Total time 2x+3x+5x+6x=16x.
If 2x = 60 then 16x = 480;
If 3x = 60 then 16x = 320;
If 5x = 60 then 16x = 192;
If 6x = 60 then 16x = 160;
Only answer choices which is not obtained is 96.
Answer: B.
Answer: (B) 96
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -15 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
(A) 90
(B) 98
(C) 106
(D) 120
(E) 136
Rationale: We see that h will be a maximum h=150 when t-3=0, that is when t=3.
At t=5, h = -15(5-3)^2 + 150 = -15(4) + 150 = 90
The answer is A.
Answer: (A) 90
Question: A Locomo's train rails across an open track at 250 kilometers per hour. A regular passenger train travels at 68% of the Locomo's train speed. If the two trains start moving from the same station at the same time, how much time longer will it take the passenger train than the Locomo's to travel 850 kilometers?
(A) 1 hour and 24 minutes.
(B) 1 hour and 36 minutes.
(C) 2 hours and 24 minutes.
(D) 2 hours and 36 minutes.
(E) 5 hours.
Rationale: Difference in time = time taken by passenger train- time taken by Locomo's train
850/(250*68) *100 - 850/250
850 (100/ 250*68 - 1/250)
850*32/ (250*68)
1.6 hrs or 1 hr and 36 mins
B is the answer
Answer: (B) 1 hour and 36 minutes.
Question: At a monthly meeting, 2/3 of the attendees were males and 3/4 of the male attendees arrived on time. If 5/6 of the female attendees arrived on time, what fraction of the attendees at the monthly meeting did not arrive on time?
(A) 1/3
(B) 1/4
(C) 3/8
(D) 2/9
(E) 5/18
Rationale: Males who did not arrive on time are 1/4*2/3 = 1/6 of the attendees.
Females who did not arrive on time are 1/6*1/3 = 1/18 of the attendees.
The fraction of all attendees who did not arrive on time is 1/6 + 1/18 = 2/9
The answer is D.
Answer: (D) 2/9
Question: Four friends, Peter, John, Quincy, and Andrew, are pooling their money to buy a $1200 item. Peter has twice as much money as John. Quincy has $20 more than Peter. Andrew has 15% more than Quincy. If they put all their money together and spend the $1200, they will have $11 left. How much money does Peter have?
(A) $320
(B) $160
(C) $200
(D) $410
(E) $325
Rationale: P= 2J ; Q= P+20 ; A= 1.15(Q)
P+J+Q+R-1200=11
P+0.5P+P+20+1.15(P+20) = 1211
P+0.5P+P+20+1.15P+23=1211
P+0.5P+P+1.15P+43=1211
P+0.5P+P+1.15P=1168
3.65P=1168
P=320
Answer:A
Answer: (A) $320
Question: If log 27 = 1.431, then the value of log 9 is:
(A) 0.934
(B) 0.945
(C) 0.954
(D) 0.958
(E) 0.944
Rationale: Explanation:
log 27 = 1.431
=log (33 ) = 1.431
=3 log 3 = 1.431
=log 3 = 0.477
log 9 = log(32 ) = 2 log 3 = (2 x 0.477) = 0.954.
ANSWER IS C
Answer: (C) 0.954
Question: Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/2 of the students who took physics left school; the chemistry students did not leave, and no fresh students came in. What fraction of all students either took biology or physics?
(A) 7/12
(B) 4/9
(C) 5/9
(D) 1/4
(E) 2/3
Rationale: Lets pick smart numbers. Total number of students: 12
Biology (1/2): 6
Chemistry (1/3): 4
Physics (1/6): 2
After leaving school
Biology: 4
Chemistry: 4
Physics: 1
New Total number of students: 9
Biology and Physics: 5
Answer 5/9 or C
Answer: (C) 5/9
Question: A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Dollar 5400 interest only for the period. The principal amount borrowed by him was:
(A) $ 18000
(B) $ 13000
(C) $ 14000
(D) $ 15000
(E) $ 19000
Rationale: D
$ 15000
Principal = Dollar (100 x 5400)/(12x3) = $ 15000.
Answer: (D) $ 15000
Question: The salary of Mr. X is 30% more than that of Mr. Y . Find what percent of Mr. Y’s salary is less than Mr. X’s?
(A) 23 1/2%
(B) 23 1/1%
(C) 23 1/3%
(D) 23 1/8%
(E) 23 1/9%
Rationale: y=100	x=130
130---------30
100---------? => 23 1/3%
Answer: C
Answer: (C) 23 1/3%
Question: Find the value of √(25/16).
(A) 5/2
(B) 3/4
(C) 2/3
(D) 1/3
(E) 5/4
Rationale: √( 25 / 16)
= √ 25 / √ 16
= 5 / 4
Answer is E.
Answer: (E) 5/4
Question: A can do a work in 8 days. B can do the same work in 16 days. If both A & B are working together in how many days they will finish the work?
(A) 3 days
(B) 16/3 days
(C) 3/4 days
(D) 9/12 days
(E) 5/7 days
Rationale: A rate = 1/8
B rate = 1/16
(A+B) rate = (1/8)+(1/16) = 3/16
A & B finish the work in 16/3days
correct option is B
Answer: (B) 16/3 days
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 300 m and they cross each other in 10sec, then the speed of each train is?
(A) 30
(B) 108
(C) 36
(D) 25
(E) 24
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (300 + 300)/10 => x = 30
Speed of each train = 30 m/sec.
= 30 * 18/5 =108km/hr.
Answer: Option B
Answer: (B) 108
Question: From 6 positive numbers and 6 negative numbers, how many groups S of 4 numbers, yielding a positive product, can be formed?
(A) 720
(B) 625
(C) 30
(D) 960
(E) 255
Rationale: Potential combinations of 4 numbers that will yield positive product
++++ 4C6
---- 4C6
++-- 2C6*2C6
4C6 + 4C6 + 2C6*2C6
S=15 +15 + 15*15 = 255=E
Answer: (E) 255
Question: Julie drives to her sister’s house and back. She takes the exact same route both ways. On the trip out she drives an average speed of 80 miles per hour. On the trip back she drives an average speed of 40 miles per hour. What is her approximate average speed for the round trip in miles per hour?
(A) 40
(B) 48.3
(C) 53.33
(D) 61.7
(E) 70
Rationale: Average speed = total distance/total time
Here distance to Julie's sister house and back is same as she takes the same route.
D = 80T1 and D=40T2
Therefore, T1 = D/80 and T2 = D/40
T1+T2 = 3d/80
Therefore, average speed = 2d/3d/80
=2d * 80/3d
Answer is 53.3 Since, the options are far away we need not solve till the decimal points
So correct answer is option C
Answer: (C) 53.33
Question: 4 dices are thrown at the same time. What is the probability of getting ONLY 2 dices showing the same face?
(A) 4/9
(B) 5/9
(C) 11/18
(D) 7/9
(E) none of the above
Rationale: Probability of getting two same faces: 1 and 1/6
For other two faces, probabilities: 5/6 and 4/6 respectively.
The dice combinations can be arranged in 4!/2! ways
Total probability = 1*1/6*5/6*4/6*4!/2! = 5/9
Answer:B
Answer: (B) 5/9
Question: 250 hundred multiples of seven are chosen at random, and 250 multiples of eight are chosen at random. Approximately what percentage of the 500 selected numbers are odd?
(A) 25.5%
(B) 26%
(C) 30%
(D) 25%
(E) 40%
Rationale: --> Multiples of 7 are 7, 14, 21, 28, 35, 42....
Out of first 4 multiples, 2 are odd; out of first 6 multiples, 3 are odd.
So approx. 50 % of the 250 multiples are odd i.e 125 multiples.
--> Similalrly, for 8 multiples are:8,16,24...
All are even so 0 % are odd.
Total odd= (125+0)/(250+250)= 125/500=1/4 = 25%
Answer D
Answer: (D) 25%
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 27 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 457 km
(B) 444 km
(C) 547 km
(D) 645 km
(E) 576 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 27 + 21 = 48
T = 12
D = 48 * 12 = 576
Answer:E
Answer: (E) 576 km
Question: A man sells an article at 5% loss. Had he sold it for Rs.60 more he could have gained 10%. What is the cost price of the article?
(A) Rs.200/-
(B) Rs.400/-
(C) Rs.450/-
(D) Rs.500/-
(E) Rs.550/-
Rationale: Short cut method:
Loss =====> 5 %
Profit ====> 10 %
~
----------------
15 % ---------> Rs.60/-
100 % --------> Rs.400/-
Option B)
Answer: (B) Rs.400/-
Question: If N is the sum of consecutive even integers w, x, y, and z, where w < x < y < z, all of the following must be true EXCEPT
(A) z - w = 3(y - x)
(B) N is divisible by 8
(C) The average of w, x, y, and z is odd
(D) N is divisible by 4
(E) w + x + 8 = y + z
Rationale: Just assume that the numbers are 2a, 2a+2, 2a+4 and 2a+6.
N = 2a + 2a+2 + 2a+4 + 2a+6 = 8a + 12
Focus on the easiest options first. You see that N is not divisible by 8. Answer (B)
Answer: (B) N is divisible by 8
Question: by combining number of small cubes, a larger cube is produced. the ratio between volume of larger cube and small cube is 1000:8 then how many small cubes are required to produce a larger cube?
(A) 100
(B) 2
(C) 5
(D) 125
(E) 80
Rationale: the ratio is a13:a23=1000:8
then number small cubes requiered is 1000/8=125
so the answre is D
Answer: (D) 125
Question: If 6Pr = 360 and If 6Cr = 15, find r ?
(A) 5
(B) 6
(C) 4
(D) 3
(E) 2
Rationale: Solution:
nPr = nCr�r!
6Pr = 15 *r!
360 =15 *r!
r! =360 /15 =24
r! = 4*3*2*1
=> r! =4!
Therefore, r = 4.
Answer: Option C
Answer: (C) 4
Question: An uneducated retailer marks all its goods at 50% above the cost price and thinking that he will still make 25% profit,offers a discount of 25% on the market price.what is the actual profit on the sales?
(A) 14.23%
(B) 56.32%
(C) 54.25%
(D) 63.45%
(E) 12.50%
Rationale: Let C.P =Rs 100.
then ,marked price =Rs100
S.P=75% of Rs 150=Rs112.50
Hence,gain%=12.50%
Ans: E
Answer: (E) 12.50%
Question: Area of square with side x is equal to the area of a triangle with base x . The altitude of the triangle is
(A) x/2
(B) x
(C) 2x
(D) 4x
(E) 3x
Rationale: x^2 =1/2 Ãƒâ€” x Ãƒâ€” h or h = 2x^2/x = 2x
Answer : C
Answer: (C) 2x
Question: The number of bacteria in a petri dish increased by 20 percent every 2 hours. If there were 72 million bacteria in the dish at 6: 00 p.m., at what time were there 50 million bacteria in the dish?
(A) 6: 00 p.m.
(B) 8: 00 p.m.
(C) 2: 00 p.m.
(D) 8: 00 a.m.
(E) 12: 00 p.m.
Rationale: Given:
he number of bacteria in a petri dish increased by 20 percent every 2 hours
There were 72 million bacteria in the dish at 6: 00 p.m
Since the bacteria is increasing by 20% every 2 hours, this means that the number is multiplied by 1.2 every 2 hours.
Required: At what time were there 50 million bacteria in the dish?
Assume that there were n intervals of 2 hours between 50 million and 72 million.
50 * (1.2)^n = 72
(12/10)^n = 72/50 = 144/100 = (12/10)^2
Hence n = 2 intervals.
Each interval was of 2 hours. Therefore, the number of hours = 4
Subtracting 4 hours from 6 PM, we get 2 PM as the answer.
Option C
Answer: (C) 2: 00 p.m.
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
(A) 1/6
(B) 1/7
(C) 1/5
(D) 1/9
(E) 1/2
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer:C
Answer: (C) 1/5
Question: A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $3,000. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
(A) $21,700
(B) $19,500
(C) $20,200
(D) $20,400
(E) $21,100
Rationale: Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 1500
Net price of the car in 02 = 18700 + 3000 = $21700
Correct Option: A
Answer: (A) $21,700
Question: The average mark of a class of thirty six students is 72. If three students whose marks are 32,28 and 34 are removed , then find the approximate average mark of the remaining students of the class.
(A) 71
(B) 74
(C) 57
(D) 76
(E) 80
Rationale: Exp. Total mark of 36 students = 72*36 = 2592,
Total mark after the removal of 3 students = 2592 –(32 +28+34 )
= 2592 – 94 = 2498
Approximate average mark = 2498/(36-3) = 2498/ 33 = 76
Answer: D
Answer: (D) 76