mathewhe/aqua_rat huggingface dataset:
Question: If x and y are integer, which of the following must also be an integer?
I. xy
II. y/x
III. x
(A) I alone
(B) II alone
(C) III alone
(D) I and III
(E) None of the above
Rationale: Let's take X = 4and Y = 3
XY which is an integer
Y/X = 3/4 Not an integer.
X alone is 4 which is an integer.
Hence D.
Answer: (D) I and III
Question: As x increases from 121 to 122, which of the following increases? I) x−1/x II) 17−1/x III) (17+x)/x
(A) I,II only
(B) I only
(C) II only
(D) III only
(E) II,III only
Rationale: On Increasing the value of x from 121 to 122
I) x−1/x will increase as 1/x will be very small and x will increase by 1 unit
II) 17−1/x Will Increase as the value of 1/x will decrease thereby increasing the value of 17-(1/x)
III) (17+x)/x = (17/x)+1 will Decrease as 1/x will decrease thereby decreasing the value of (17/x)
Answer:A
Answer: (A) I,II only
Question: 50 men can complete a work in 65 days.Five days after started the work, 20 men left the group. In how many days can the remaining work be completed?
(A) 140 days.
(B) 140 days.
(C) 120 days.
(D) 100 days.
(E) 110 days.
Rationale: D
100 days.
After 5 days, the following situation prevails.
50 men can complete the work in 60 days.
30 men can complete the work in ? days.
M1 D1 = M2 D2
=> 50 * 60 = 30 * D2
=> D2 = (50 * 60)/30 = 100 days.
Answer: (D) 100 days.
Question: The odds in favour of an events are 3:5. The probability of occurrence of the event is
(A) 3/8
(B) 2/7
(C) 1/3
(D) 2/5
(E) 6/7
Rationale: Number of cases favourable to E = 3
Total number of cases = 3+5 = 8
P(E) = 3/8
Answer is A
Answer: (A) 3/8
Question: Two pipes A and B can fill a tank in 15 min and 20 min respectively. Both the pipes are opened together but after 4 min, pipe A is turned off. What is the total time required to fill the tank?
(A) 14 min 70 sec
(B) 14 min 60 sec
(C) 14 min 47 sec
(D) 14 min 40 sec
(E) 13 min 40 sec
Rationale: Part filled in 4 minutes = 4(1/15 + 1/20) = 7/15
Remaining part = 1 - 7/15 = 8/15
Part filled by B in 1 minute = 1/20
1/20 : 8/15 :: 1 ; x
x = 8/15 * 1 * 20 = 10 2/3 min = 10 min 40 sec.
The tank will be full in (4 min. + 10 min. 40 sec)
= 14 min 40 sec.
Answer: D
Answer: (D) 14 min 40 sec
Question: There are two boxes,one containing 39 red balls & the other containing 26 green balls.you are allowed to move the balls b/w the boxes so that when you choose a box random & a ball at random from the chosen box,the probability of getting a red ball is maximized.this maximum probability is
(A) 0.9
(B) 0.8
(C) 0.5
(D) 0.7
(E) 0.2
Rationale: Ans: Very interesting question.
As we are allowed to move the balls, we keep only one red ball in first box and move all the remaining balls to the second box
So fist box contains 1 redball, second box contains 38 red + 26 green = 64 balls
Probability of choosing any box is 1/ 2.
So probability of taking one red ball = 12×(1)+12(3864)≃0.8
Answer:B
Answer: (B) 0.8
Question: A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.0 km long?
(A) 2.5
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: D = 25 * 60 + 1000 = 2500 m
T = 2500/60 * 18/5 = 150 sec = 2.5 mins
Answer: A
Answer: (A) 2.5
Question: When positive integer W is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?
(A) a. k + 1
(B) b. k -11
(C) c. 4k + 2
(D) d. (k-3)/3 +2
(E) e. W/3
Rationale: When positive integer W is divided by 6 the remainder is 3
So, W could equal 3, 9, 15, 21, etc
let's TEST W =3
a.3+ 1 = 4 (EVEN)
b.3-11 = -8 (EVEN)
c. 4(3) + 2 = 14 (EVEN)
d. (3-3)/3 +2 = 2 (EVEN)
At this point, we can already see the answer must be E.
Let's check E forfun
e.3/3 = 1 (ODD)
Great!
Answer: E
Answer: (E) e. W/3
Question: Find the amount on Rs.8000 in 9 months at 20% per annum, if the interest being compounded quarterly?
(A) 9287
(B) 9261
(C) 9229
(D) 9285
(E) 2788
Rationale: A = 8000(21/20)3
= 9261
Answer: B
Answer: (B) 9261
Question: If 0 < A < Y, A is an odd number and Y is a prime number, which of the following can be the value of A + Y ?
(A) 11.
(B) 13.
(C) 17.
(D) 10.
(E) 7.
Rationale: If A is odd ,implies a(odd)+y(odd/even prime)=(Even/Odd)
If Y is even, the 2 is the even prime , therefore y=2A=1 since 0<A<Y therefore A+Y =3. But 3 is not an option
which implies y is odd,
Now A(odd)+Y(odd)=Even
10 is the only option that is even=D
Answer: (D) 10.
Question: One vessel contains a mixture of 5 parts pure wine and 3 parts soda, whereas the other vessel contains a mixture of 7 parts pure wine and 5 parts soda. Compare the strength of the wine.
(A) 35;36
(B) 7 : 8
(C) 15 : 14
(D) 14 : 5
(E) None of these
Rationale: 5/8 : 7/12
LCM of 8,12 = 24
(5/8)*24 : (7/12)*24
15:14
Answer is C.
Answer: (C) 15 : 14
Question: Employees at a company will vote for an executive team of five people from eight qualified candidates. The executive team consists of a president, a treasurer, and three warrant officers. If an executive team is considered different if any of the same people hold different offices, then how many possible executive teams S could be selected from the eight candidates?
(A) 56
(B) 120
(C) 210
(D) 1120
(E) 6720
Rationale: If an executive team is considered different if any of the same people hold different offices,....
so you will not have answer as 6720..
president could be by any of 8 person..
treasurer could be any out of remaining 7 person..
remaining three order does not matter, so we have to choose 3 out of 6=6c3=20..
total ways S= 8*7*20=1120..
ans D...
Answer: (D) 1120
Question: Find the least number of five digits which is exactly divisible by 12, 15 and 18?
(A) 1080
(B) 10080
(C) 10025
(D) 11080
(E) 12000
Rationale: LCM = 180
180) 10000 (55
9900
---------
100
10000 + 180 - 100 = 10080
ANSWER:B
Answer: (B) 10080
Question: A waiter's salary consists of his salary and tips. During one week his tips were 5/2 of his salary. What fraction of his income came from tips ?
(A) 4/9
(B) 5/4
(C) 5/8
(D) 5/7
(E) 6/9
Rationale: Income = salary (s) +tips = s + s*5/2 = s*7/2
Tips = s*7/2
fraction of his income came from tips = (s*5/2)/(s*7/2)= 5/7
ANSWER:D
Answer: (D) 5/7
Question: A can do a work in 40days, B in 60days. A alone start the work after 10days he left work. In how many days B can finish the work?
(A) 20days
(B) 15days
(C) 30days
(D) 45days
(E) 50days
Rationale: 10days work of A = 10/40 = 1/4
remaining work = 1-1/4 = 3/4
B can finish 3/4 work = 60*3/4 = 45days
Answer is D
Answer: (D) 45days
Question: When N is divided by 10 the remainder is 1 and when N is divided by 3 the remainder is 2. What is the remainder K when N is divided by 30?
(A) (a) 4
(B) (b) 7
(C) (c) 11
(D) (d) 13
(E) (e) 17
Rationale: N ends in the digit 1 because when N is divided by 10, the remainder is 1. Since N ends in 1, the remainder K when N is divided by 30 also ends in a 1. 11 is the only choice which ends in a 1.C
Answer: (C) (c) 11
Question: For every positive integer n, the nth term of a sequence is the total sum of three consecutive integers starting at n. What is the total sum of terms 1 through 60 of this series?
(A) 5330
(B) 5670
(C) 5990
(D) 6240
(E) 6550
Rationale: Each term of the series has the form (n+n+1+n+2) = 3n+3
Since the series goes from 1 to 60, the sum of the series is:
3(1+2+...+60) + 60(3) =
3(60)(61)/2 + 60(3) =
90*61 + 180 = 5670
The answer is B.
Answer: (B) 5670
Question: Which of the following is closer to (6!+4!)*(6!-4!)?
(A) 587945
(B) 647280
(C) 587920
(D) 658230
(E) 954120
Rationale: Notice that 6! = (6*5)(4!)
(6!+4!)*(6!-4!)=[6!(30+1)]*[6!(30-1)]
= 21/19
≈ 647280
Answer: B
Answer: (B) 647280
Question: |5 - 2| - |6 - 9| = ?
(A) 3
(B) 2
(C) 1
(D) 0
(E) 4
Rationale: |5 - 2| - |6 - 9| = | 3 | - | -3 | = 3 - 3 = 0
correct answer D
Answer: (D) 0
Question: In business, A and C invested amounts in the ratio 3:2, whereas the ratio between amounts invested by A and B was 3:4, If Rs 30,000 was their profit, how much amount did B receive.
(A) 1235
(B) 62896
(C) 6666
(D) 8974
(E) 5626
Rationale: Explanation:
A:B = 3:4 = 3:4
=> A:C = 3:2 = 3:2
=> A:B:C = 3:4:2
C share = (2/9)*30000
= 6666
Option C
Answer: (C) 6666
Question: A wheel rotates 10 times every minute and moves 20 cm during each rotation. How many ems does the wheel move in 1 hour?
(A) 20000
(B) 14000
(C) 23000
(D) 120000
(E) None of these
Rationale: Explanation :
Number of wheel moves in 1 hour = 10 * 60 = 600distance moved = 600 * 200 = 12000
Answer : D
Answer: (D) 120000
Question: There are 100 freshmen at a particular college, all of whom must take at least one of the three core classes: Art, Biology, and Calculus. Of these freshmen, 13 take only Biology, 10 take only Calculus, 5 take all three classes, and 20 take Art and exactly one of the other two core classes. If the number of freshmen who take only Art is 3 times the number of freshmen who take every core class except Art, how many freshmen take Art?
(A) 25
(B) 64
(C) 36
(D) 48
(E) 61
Rationale: Make a venn diagram to get a clear picture. Look at the diagram:
Each letter represents only one color. b represents the people who take only Art. d represents people who take only Art and Bio etc.
d + f = 20 (People who take Art and one other class)
b = 3e (people who take only Art is 3 times the people who take Bio and Calculus)
13 + 10 + 5 + b + d + e + f = 100 (Total people)
b + b/3 = 52
b = 39
Number of freshmen who take Art = 39 + 20 + 5 = 64
Answer B
Answer: (B) 64
Question: Find the value of x from logx 100 = 2
(A) 10
(B) 12
(C) 13
(D) 14
(E) 15
Rationale: solution:
logb 1000 = 3
We can write it as,
b3 = 1000
b3 = 103
So from the above equation
b = 10
ANSWER IS A
Answer: (A) 10
Question: The bankerâ€™s discount of a certain sum of money is Rs. 90 and the true discount on the same sum for the same time is Rs. 60. The sum due is
(A) 210
(B) 180
(C) 360
(D) 450
(E) None
Rationale: Sol.
Sum = B.D. * T.D. / B.D. - T.D. = Rs.[90 * 60 / 90 - 60] = Rs. [90 * 60 / 30] = Rs. 180
Answer B
Answer: (B) 180
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 4 km in stationary water
(A) 40 min
(B) 1hr
(C) 1hr 15 min
(D) 1hr 30 min
(E) 4 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(4/4)=1 hr
Answer(B)
Answer: (B) 1hr
Question: A shopkeeper increases the price of an article by X% and then decreases it by X%. As a result the price of the article is reduced by $180. After one more such change the price is further reduced by $153 Find the original price of the article.
(A) $1200
(B) $1100
(C) $1400
(D) $1000
(E) $1500
Rationale: Given:
After a% decrease the price of the article is reduced by $180 --> pa=180;
After one more such change the price is further reduced by $153. After the first decrease the price became $(p−180), thus (p−180)a=153--> pa−180a=153a=15--->a=15 --> p∗0.15=180--> p=1,200
Answer: A.
Answer: (A) $1200
Question: A question paper has 2 parts, A & B, each containing 7 questions. If a student has to choose 5 from part A & 4 from part B, in how many ways can he choose the questions?
(A) 1100
(B) 1200
(C) 1235
(D) 1354
(E) 735
Rationale: There 7 questions in part A out of which 5 question can be chosen as = 7C5.
Similarly, 4 questions can be chosen from 7 questions of Part B as = 7C4.
Hence, total number of ways,
=7C5*7C4
=[7!/(2!5!)]*[7!/(3!*4!)]
= {21}*{7*6*5*4/(4*3*2*1)}
= 735.
E
Answer: (E) 735
Question: If x = 3 and y = −2, what is the value of (x − 2y)^y?
(A) −100
(B) 0.02
(C) 0.25
(D) 4
(E) 8
Rationale: Quickly we can spot that answer is neither integer nor negative. Eliminate A, DE
Answer: B
Answer: (B) 0.02
Question: How many different positive integers are factors of 324 ?
(A)  9
(B)  16
(C)  25
(D)  36
(E)  49
Rationale: 18×18=6^2 × 3^2
So total factors = (5+1)(5+1) = 36
Answer: D
Answer: (D)  36
Question: The average monthly salary of the employees of a firm is Rs.60 out of the employees 12 officers get an average of Rs.400 per month and the rest an average of Rs. 56 per month , Find the number of emp
(A) 1032
(B) 2766
(C) 2882
(D) 2788
(E) 2772
Rationale: Actual average salary of 12 officers = 400
\inline \fn_jvn \therefore Total salary of 12 officers = 400 x 12 = 4800
Average of these 12 officers as a whole =60
Total salary of 12 officers as a whole = 60 x 12 = 720
The total salary of rest = 4800 - 720 = 4080
Difference in average of the rest of officers = 60 - 56 = 4
Rest of the officers = \inline \fn_jvn \frac{4080}{4}=1020
Total number of employees = 1020 + 12 = 1032
ANSWER:A
Answer: (A) 1032
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 78 kg and 93 kg join the group. Find the initial number of members in the group?
(A) 21
(B) 22
(C) 23
(D) 24
(E) None of these
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 78 + 93 = 51(n + 2) => 51n - 48n = 69 => n = 23
Therefore there were 23 members in the group initially.
ANSWER:C
Answer: (C) 23
Question: Club X has more than 30 but fewer than 60 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: The number of members is 4j+3 = 5k+3.
Let's start at 4(7)+3 = 31 and keep adding 4 until we find a number in the form 5k+3.
31, 35, 39, 43 = 5(8) + 3
The club has 43 members.
43/6 = 6(7) + 1
The answer is A.
Answer: (A) 1
Question: An old priest fell on a bottom of the well of a church.
The well is 19 inches deep.
At day time, the old priest climbs 5-inches but when at dark he slip back 4 inches.
In how many days priest will come out of the well ?
(A) 15-days
(B) 14-days
(C) 11-days
(D) 19-days
(E) 10-days
Rationale: A
15-days
In 14-days, he will climb 14-inch and when he climbs 5 inch more, he will be out of the well :-)
Answer: (A) 15-days
Question: Two trains, one from P to Q and the other from Q to P, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is
(A) 4:3
(B) 3:4
(C) 2:4
(D) 4:2
(E) 2:5
Rationale: Req ratio = root(16):root of(9)=4:3
ANSWER A
Answer: (A) 4:3
Question: If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). The temperature required to boil liquid A and liquid B differed by 35 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?
(A) a) 17
(B) b) 13
(C) c) 25
(D) d) 45
(E) e) 81
Rationale: The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case). Just looking at the answer choices you can pick A which is the only number near half of 35. The other answer choices are too far apart so no need to calculate.
Answer: (A) a) 17
Question: Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?
(A) 3 hours
(B) 6 hours
(C) 4 hours
(D) 8 hours
(E) 10 hours
Rationale: Number of pages typed by Ronald in one hour = 32/6 = 16/3
Number of pages typed by Elan in one hour = 40/5 = 8
Number of pages typed by both in one hour = ((16/3) + 8) = 40/3
Therefore, time taken by both to type 110 pages = 110 x 3/40 = 8 hours.
ANSWER:D
Answer: (D) 8 hours
Question: A copy machine, working at a constant rate, makes 30 copies per minute. A second copy machine, working at a constant rate, makes 55 copies per minute. Working together at their respective rates, how many copies do the two machines make in half an hour ?
(A) 90
(B) 2,700
(C) 4,500
(D) 2,550
(E) 324,000
Rationale: Together the two machines make 30+55=85 copies per minute. So, in half an hour they will make 85*30=2,550 copies.
Answer: D.
Answer: (D) 2,550
Question: Find the value of x. (47% of 1442 - 36% of 1412) + 63 = x?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: C) 3
Answer: (C) 3
Question: How much 60% of 50 is greater than 40% of 30?
(A) 18
(B) 99
(C) 66
(D) 55
(E) 71
Rationale: (60/100) * 50 – (40/100) * 30
30 - 12 = 18
Answer: A
Answer: (A) 18
Question: A marching band of 240 musicians are to march in a rectangular formation with s rows of exactly t musicians each. There can be no less than 8 musicians per row and no more than 30 musicians per row. How many different rectangular formations Z are possible?
(A) 3
(B) Z=4
(C) Z=5
(D) Z=6
(E) Z=8
Rationale: The combinations could be {(1,240),(2,120),(3,80),(4,60),(5,48),(6,40),(8,30),(10,24),(12,20),)15,16),(16,15),(20,12),(24,10),(30,8),(40,6),(48,5),(60,4),(80,3),(120,2),(240,1)}
Of these we are told 8<=t<=30 So we can remove these pairs, and we are left only with.
{(8,30,(10,24),(12,20),(15,16),(16,15),(20,12),(24,10),(30,8)}
Hence 8.E
Answer: (E) Z=8
Question: A 80 gallon solution of salt and water is 10% salt. How many gallons of water must be added to the solution in order to decrease the salt to 8% of the volume?
(A) 20
(B) 12
(C) 13
(D) 14
(E) 16
Rationale: Amount of salt = 8.0
Assume x gallons of water are added.
8.0 / 80 + x = 8/100
800 = 8x + 640
8x = 160
x = 20
Correct Option: A
Answer: (A) 20
Question: Find the amount on Rs.5000 in 2 years, the rate of interest being 4% per first year and 5% for the second year?
(A) 5418
(B) 5498
(C) 5460
(D) 5179
(E) 5418
Rationale: 5000 * 104/100 * 105/100
=> 5460
Answer:C
Answer: (C) 5460
Question: The sum of four consecutive even numbers is 84. What would be the largest number?
(A) 33
(B) 88
(C) 24
(D) 123
(E) 12
Rationale: Let the four consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1)
Their sum = 8x - 4 = 84 => x = 11
Smallest number is: 2(x +1) = 24.
Answer: C
Answer: (C) 24
Question: If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
(A) 5:9
(B) 5:5
(C) 5:3
(D) 5:2
(E) 5:1
Rationale: Let 40% of A = 2/3 B. Then,
40A/100 = 2B/3 => 2A/5 = 2B/3
A/B = (2/3 * 5/2) = 5/3
A:B = 5:3.
Answer:C
Answer: (C) 5:3
Question: Out of seven numbers, average of first six number is 40 and average of last six number is 35. the first number is 55. What is the difference between first and last number?
(A) 30
(B) 37
(C) 41
(D) 59
(E) None
Rationale: Let the seven numbers be represented by
{a,b,c,d,e,f,g}
let sum(b-f) be the sum of numbers b through f.
For the average of the first six we have
(a + sum(b-f))/6 = 40
(a + sum(b-f)) = 240
We are given that the first number, a, is 55, so we have
sum(b-f) = 240 - a
sum(b-f) = 240 - 55
sum(b-f) = 185
Now for the average of the last six numbers we have
(sum(b-f) + g)/6 = 35
(sum(b-f) + g) = 210
185 + g = 210
g = 210 - 185
g = 25
The first number is 55 and the last number is 25 so, their difference is 30.
Answer A
Answer: (A) 30
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 4 to 5. 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) 168
(B) 210
(C) 280
(D) 420
(E) 240
Rationale: A:B:C:D=2x:3x:4x:5x, for some positive number x. Total time 2x+3x+4x+5x=14x.
If 2x = 60 then 14x = 420;
If 3x = 60 then 14x = 280;
If 4x = 60 then 14x = 210;
If 5x = 60 then 14x = 168;
Only answer choices which is not obtained is 240.
Answer: E.
Answer: (E) 240
Question: The lunch menu at a certain restaurant contains 4 different entrees and 5 different side dishes. If a meal consists of 1 entree and 2 different side dishes, how many different meal combinations W could be chosen from this menu?
(A) 10
(B) 20
(C) 40
(D) 80
(E) 100
Rationale: W=4C1 * 5C2
= 4 * (5*4*3!)/(3!2!)
= 4 * 10
= 40
Answer - C
Answer: (C) 40
Question: When we multiply a certain two digit number by the
sum of its digits 405 is achieved. If we multiply the
number written in reverse order of the same digits
by the sum of the digits,we get 486.Find the number?
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: Let the number be x y.
When we multiply the number by the sum of its digit
405 is achieved.
(10x+y)(x+y)=405....................1
If we multiply the number written in reverse order by its
sum of digits we get 486.
(10y+x)(x+y)=486......................2
dividing 1 and 2
(10x+y)(x+y)/(10y+x)(x+y) = 405/486.
10x+y / 10y+x = 5/6.
60x+6y = 50y+5x
55x=44y
5x = 4y.
From the above condition we conclude that the above
condition is satisfied by the second option i e b. 45.
ANSWER : B 45
Answer: (B) 45
Question: Find the value of (85 + 32/113) × 113
(A) 9263
(B) 9244
(C) 9636
(D) 9623
(E) 9637
Rationale: =(85 + 32/113) × 113
=(9605 + 32)/113× 113
=9637/113× 113
=9637
Answer is E.
Answer: (E) 9637
Question: For an agricultural experiment, 500 seeds were planted in one plot and 200 were planted in a second plot. If exactly 30 percent of the seeds in the first plot germinated and exactly 50 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated?
(A) 35.7%
(B) 25%
(C) 32%
(D) 30.8%
(E) 60%
Rationale: From the first plot 0.30*500=150;
From the second plot 0.50*200=100;
Total percent = (150+100)/(500+200) = 0.357.
Answer: A.
Answer: (A) 35.7%
Question: There are 2 sections A and B in a class, consisting of 40 and 30 students respectively. If the average weight of section A is 50kg and that of section B is 60kg, Find the average of the whole class?
(A) 50.78kg
(B) 49.32kg
(C) 61.67kg
(D) 69.15kg
(E) 54.28kg
Rationale: Total weight of 40+30 students = 40*50 + 30*60 = 2000+1800
Average weight of the class is = 3800/70 = 54.28 kg
Answer is E
Answer: (E) 54.28kg
Question: In a jar there are balls in different colors: blue, red, green and yellow.
The probability of drawing a blue ball is 1/8.
The probability of drawing a red ball is 1/5.
The probability of drawing a green ball is 1/7.
If a jar cannot contain more than 500 balls, how many yellow balls are in the Jar?
(A) 125.
(B) 124.
(C) 133.
(D) 140.
(E) 149.
Rationale: We need to get some number which is less than 500 and exactly divisible by 8,5 and 7
Lets take LCM of three balls 8,5 and 7 = 280.
The probability of drawing a blue ball is 1/8...For every 8 balls we get 1 BLUE ball then out of 280 balls we get 35 BLUE balls.
The probability of drawing a red ball is 1/5...For every 5 balls we get 1 RED ball then out of 280 balls we get 56 REB balls.
The probability of drawing a green ball is 1/7. For every 7 balls we get 1 GREEN ball then out of 280 balls we get 40 GREEN BALLS.
Then out of 280 - ( 35 + 56 + 40 ) = 149 YELLOW balls.
IMO option E is correct.
Answer: (E) 149.
Question: If x - 5 > 2 and x + 3 < 7, the value of x must be between which of the following pairs of numbers?
(A)  -3 and 10
(B)  -3 and 4
(C)  2 and 7
(D)  3 and 4
(E)  3 and 10
Rationale: Let’s isolate x in each inequality.
x - 5 > 2
x > 3
Next we simplify x +3 < 7.
x +3 < 7
x < 4
We know that x is greater than 3 and less than 4.
The answer is D.
Answer: (D)  3 and 4
Question: The average weight of a group of persons increased from 48 kg to 51 kg, when two persons weighing 88 kg and 93 kg join the group. Find the initial number of members in the group?
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: Let the initial number of members in the group be n.
Initial total weight of all the members in the group = n(48)
From the data,
48n + 88 + 93 = 51(n + 2) => 51n - 48n = 79 => n = 26
Therefore there were 26 members in the group initially.
ANSWER:D
Answer: (D) 26
Question: If 20 toys cost Rs, 234, what do 35 toys cost?
(A) 409.5
(B) 564.5
(C) 546.5
(D) 654.5
(E) None of them
Rationale: Let the required cost be Rs. x. Then,
More toys, More cost	(Direct Proportion)
. = x=(35 X 234)/20=409.50
Answer is A
Answer: (A) 409.5