mathewhe/aqua_rat huggingface dataset:
Question: Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?
I. Stephanie
II.Brian
III. Regine
(A) I only
(B) II only
(C) I or III only
(D) I or II only
(E) I, II, or III
Rationale: Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.
Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.
There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.
Answer: C.
Answer: (C) I or III only
Question: The average monthly salary of 20 employees in an organisation is Rs. 1200. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?
(A) 3600
(B) 3890
(C) 3300
(D) 2789
(E) 2891
Rationale: Explanation:
Manager's monthly salary Rs. (1300 * 21 - 1200 * 20) = Rs. 3300.
Answer: C
Answer: (C) 3300
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
(A) 27 7/6
(B) 27 7/5
(C) 27 7/4
(D) 27 7/9
(E) 27 7/3
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer:D
Answer: (D) 27 7/9
Question: Car A travels at three times the average speed of car B. Car A started to travel at 12:00 o'clock, car B started to travel at 16:00 o'clock. What is the speed of car B (in Km/h) if the total distance that both cars traveled until 18:00 was 2000 Km?
(A) 10.
(B) 25.
(C) 30.
(D) 38.
(E) 100.
Rationale: Total distance= Distance travelled by A +Distance travelled by car B
Distance= speed*time
Distance of A= 3x * 6
Distance of B= x*2
(3x * 6) + (x*2) = 2000
x= 100 KM/hr
E is the answer
Answer: (E) 100.
Question: What will come in place of the x in the following Number series? 5,28,57,88,125
(A) 125
(B) 153
(C) 166
(D) 187
(E) 193
Rationale: 28=23+5
57=29+28
88=31+57
125=37+88
166=41+125
=166
C
Answer: (C) 166
Question: Two numbers N and 12 have LCM = 48 and GCF = 8. Find N.
(A) 24
(B) 34
(C) 44
(D) 54
(E) 32
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
12 × N = 48 × 8
N = 48 × 8 / 12 = 32
correct answer E
Answer: (E) 32
Question: 20% of a number is more than 40% of 140 by 80. Find the number?
(A) 680
(B) 620
(C) 652
(D) 520
(E) 458
Rationale: (20/100) * X – (40/100) * 140= 80
1/5 X = 136
X = 680
Answer:A
Answer: (A) 680
Question: A person want to give his money of $1800 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?
(A) $700
(B) $600
(C) $900
(D) $500
(E) $400
Rationale: B's share = 1800*3/9 = $600
Answer is B
Answer: (B) $600
Question: A car was driving at 60 Km/h for 20 minutes, and then at 90Km/h for another 40 minutes. What was its average speed?
(A) 80.
(B) 75
(C) 70
(D) 65.
(E) 54.
Rationale: driving at 60 Km/h for 20 minutes ,distance covered = 60*1/3=20 km
driving at 90 km/h for 40 minutes ,distance covered = 90*2/3=60 km
average speed = total distance/total time = 80/1 = 80 km/h
ANSWER:A
Answer: (A) 80.
Question: A seller has 1000 kg of rice part of which he sells at 8% profit and the rest at 18% profit. He gains 14%. The quantity sold at 18% profit is?
(A) 200 kg
(B) 300 kg
(C) 400 kg
(D) 600 kg
(E) 800 kg
Rationale: By rule of alligation,
Profit% by selling 1st part	Profit% by selling 2nd part
8	18
Net % profit
14
18-14=4	14-8=6
=> Quantity of part1 : Quantity of part2 = 4 : 6 = 2 : 3
Total quantity is given as 1000 kg. So quantity of part2 (quantity sold at 18% profit)
=1000×35
= 600 kg
D
Answer: (D) 600 kg
Question: N = 1/3 + 1/4
What is the value of N?
(A) 7/12
(B) 1/6
(C) 1/8
(D) 5/17
(E) 12/7
Rationale: To sum 1/3 and 1/4
Multiply both sides by 12
12 * N = 12 * 1/3 + 12 * 1/4
12 * N = 4 + 3
N = 7/12
Ans: A
Answer: (A) 7/12
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. x = 0
II. y = 0
III. x = y
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II, and III
Rationale: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer D
Answer: (D) I and III only
Question: If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be?
(A) 2
(B) 4
(C) 6
(D) 7
(E) 8
Rationale: Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3.
x = 2.
A)
Answer: (A) 2
Question: Which of the following fractions is less than 1/3
(A) 22/62
(B) 15/46
(C) 15/39
(D) 2/3
(E) 1
Rationale: 1/3=0.3333333
22/62=0.35>0.3333
15/46=0.331
ANSWER:B
Answer: (B) 15/46
Question: A monkey tries to ascend a greased pole 14 m high. He ascends 2 m in first minute and slips 1 min next alternate minute. If he continues to ascend in this fashion, how long does he take to reach the top?
(A) 22
(B) 24
(C) 25
(D) 26
(E) 30
Rationale: Monkey ascends 2 m in 1 minutes and slips 1 m in next minute.
It means he ascends
2 - 1 = 1 m in every two minutes.
Take 2 minutes = 1 unit of time.
It will take 12 unit of time to climb 12 m of the pole.
In next 1 minute, he will covered 2 m and reached the top. So,
Total time = 12 unit + 1 = 24 +1 = 25 minutes.
ANSWER : OPTION C
Answer: (C) 25
Question: Seven years ago, the combined ages of Amir and Akshay was twice that of Saif. If the sum of the ages of Akshay and Amir, fifteen years hence, is 98 years, what is the present age of Saif?
(A) 27 yr
(B) 35 yrs
(C) 34 yrs
(D) 49 yr
(E) 29 yr
Rationale: Amir -- M
Akshay ..K
Saif .. S
M+K =2S
M+K+30= 98
M+K=68
S= 68/2=34 yrs
ANSWER:C
Answer: (C) 34 yrs
Question: If each digit in the set of A = {1,2,3,4,5,6,7,8} is exactly used once, in how many ways can the digits be arranged such that the 2 and 5 are not adjacent?
(A) 8! / 7!
(B) 8! - 7!
(C) 6*7!
(D) 8!/2!
(E) 7!
Rationale: The answer should be the (total arrangements) - (arrangements when 2 and 5 are adjacent).
The number of ways to arrange 8 units is 8!
If we think of 2 and 5 as one single unit, the number of arrangements is 7!
Note that 2 and 5 can have two arrangements, so we multiply by 2 to get 2*7!
The total number of valid arrangements is 8! - 2*7! = 8*7! - 2*7! = 6*7!
The answer is C.
Answer: (C) 6*7!
Question: A producer of tea blends two varieties of tea from two tea gardens one costing Rs 18 per kg and another Rs 20 per kg in the ratio 5 : 3. If he sells the blended variety at Rs 21 per kg, then his gain percent is
(A) 12%
(B) 13%
(C) 14%
(D) 15%
(E) 16%
Rationale: Explanation:
Suppose he bought 5 kg and 3 kg of tea.
Cost Price = Rs. (5 x 18 + 3 x 20) = Rs. 150.
Selling price = Rs. (8 x 21) = Rs. 168.
Profit = 168 - 150 = 18
So, Profit % = (18/150) * 100 = 12%
Option A
Answer: (A) 12%
Question: 7 teams compete in a track competition. If there are 15 events in the competition, no event ends in a tie, and no team wins more than 3 events, what is the minimum possible number of teams that won at least one event?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 3(max wins) x 5 = 15 (5 teams win three events)
The answer is C.
Answer: (C) 5
Question: Each factor of 240 is inscribed on its own plastic ball, and all of the balls are placed in a jar. If a ball is randomly selected from the jar, what is the probability that the ball is inscribed with a multiple of 15?
(A) 1/16
(B) 5/42
(C) 1/8
(D) 3/16
(E) 1/4
Rationale: the # of factors 240 has is 20;
so out of 20 factors only four are multiples of 15: 15, 30, 60, 120 and 240, itself;
So, the probability is 5/20=1/4.
Answer: E.
Answer: (E) 1/4
Question: If Jake loses 35 pounds, he will weigh thrice as much as his sister. Together they now weigh 275 pounds. What is Jake's present weight, in pounds?
(A)  131
(B)  135
(C)  139
(D)  147
(E)  188
Rationale: J = Jake’s current weight, in pounds
S = Sister’s current weight, in pounds
We are told that “If Jake loses 8 pounds, he will weigh twice as much as his sister.We put this into an equation:
J – 35 = 3S
J = 3S + 35 (Equation 1)
Next, we are told that “Together they now weigh 275 pounds.” We can also put this into an equation.
J + S = 275 (Equation 2)
To solve this equation, we can substitute 2S + 8 from Equation 1 for the variable J in Equation 2:
3S + 35 = 275-S
4S = 240
S = 60
J + 60 = 275
J = 215
Answer: E
Answer: (E)  188
Question: If the radius of a circle is diminished by 10%, then the area is diminished by:
(A) 200%
(B) 210%
(C) 300%
(D) 310%
(E) None of these
Rationale: Explanation:
Let the original radius be R cm. New radius = 2R
Area=πR2
New Area =π2R2
=4πR2
Increase in area =(4πR2−πR2)=3πR2
Increase percent =3πR2 /πR2∗100=300%
Option C
Answer: (C) 300%
Question: The distance from Steve's house to work is 28 Km. On the way back Steve drives twice as fast as he did on the way to work. Altogether, Steve is spending 6 hours a day on the roads. What is Steve's speed on the way back from work?
(A) 5.
(B) 10.
(C) 14.
(D) 15.
(E) 20.
Rationale: Time is in the ratio 2:1 :: to: fro office
Therefore, 2x+1x=6 hrs
Time take to come back - 2 hrs, distance travelled - 28km => Speed = 14kmph
C
Answer: (C) 14.
Question: Which of the following numbers is divisible by 4?
(A) 27767
(B) 10224
(C) 26778
(D) 26679
(E) 26711
Rationale: 10224. This is the only option with last two digits divisible by 4
Answer:B
Answer: (B) 10224
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
(A) 18
(B) 27
(C) 40
(D) 37
(E) 29
Rationale: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
Answer: C
Answer: (C) 40
Question: A no. when divided by the sum of 555 and 445 gives 2times their difference as quotient & 30 as remainder. Find the no. is?
(A) 122456
(B) 145778
(C) 456678
(D) 235467
(E) 220030
Rationale: (555 + 445) * 2 * 110 + 30 = 220000 + 30 = 220030
E
Answer: (E) 220030
Question: How many three digits no. can be formed also including the condition that the no. can have at least two same digits ?
(A) 458
(B) 249
(C) 251
(D) 252
(E) 254
Rationale: total 3 digit no. is-9*10*10=900
and total no. of non repeated digits are=9*9*8=648
So the total no. of repeated digits(2 & 3 repeated)=900-648=252
ANSWER:D
Answer: (D) 252
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 16 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) 738 km
(B) 444 km
(C) 849 km
(D) 935 km
(E) 949 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 16 + 21 = 37
T = 12
D = 37 * 12 = 444
Answer:B
Answer: (B) 444 km
Question: Calculate the fourth proportional to 6.1, 7.2 and 9.3?
(A) 2.98
(B) 11.98
(C) 19.98
(D) 10.98
(E) 1.98
Rationale: Explanation:
Formula = Fourth propotional = (b × c)/a
A = 6.1 , B = 7.2 and C = 9.3
(7.2 × 9.3)/6.1 = 10.98
Answer: Option D
Answer: (D) 10.98
Question: Find the greatest number that will divide 400, 435 and 541 leaving 9, 10 and 14 as remainders respectively
(A) 19
(B) 17
(C) 13
(D) 9
(E) 8
Rationale: Explanation:
Answer will be HCF of (400-9, 435-10, 541-14)
HCF of (391, 425, 527) = 17
Option B
Answer: (B) 17
Question: Find the odd man out
864, 420, 200, 86, 40, 16, 6
(A) 420
(B) 200
(C) 16
(D) 40
(E) 86
Rationale: 6x2+4=16
16x2+8=40
40x2+12=92
92x2+16=200.. and so on. 86
ANSWER:E
Answer: (E) 86
Question: A man can row downstream at the rate of 12 Km/hr and upstream at 6 Km/hr. Find man's rate in still water and the rate of current?
(A) 9,6
(B) 6,3
(C) 9,3
(D) 6,6
(E) None of these
Rationale: Explanation:
Rate of still water = 1/2 (12 + 6) = 9 Km/hr
Rate of current = 1/2 (12-6) = 3 Km/hr
Answer: Option C
Answer: (C) 9,3
Question: A shopkeeper sold an book 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) 140
(B) 120
(C) 130
(D) 110
(E) 150
Rationale: C
130%
Let C.P. be $100.
Then, S.P. = $123.50
Let marked price be $x. Then, 95/100 x = 123.50
x = 12350/95 = $130
Now, S.P. = $130, C.P. = $100
Profit % = 30%.
Answer: (C) 130
Question: Jonathan’s grandparents lend $50,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?
(A) 50,000∗0.1^5
(B) 50,000∗0.5
(C) 50,000∗1^.5
(D) 50,000∗1.5
(E) (50,000∗0.1)^5
Rationale: if you are like me and have used S.I = P x R x T formula in school, while the question is asking for Amount in 5 years. so (D) 50,000∗ 1.5
Ans : D
Answer: (D) 50,000∗1.5
Question: A girl sold her pen for Rs.39 and got a percentage of profit numerically equal to the cost price. The cost price of that pen is:
(A) 130
(B) 90
(C) 60
(D) 30
(E) 20
Rationale: Let Cost Price was Rs. X then % profit must be X%.
Selling Price = Rs. 39
Cost price + profit = 39
X + X% of X = 39
X + (X^2)/100 = 39
100 X + X^2 = 3900
X^2 + 100X - 3900 = 0
X^2 +130X - 30X - 3900 = 0
X = -130, 30
Cost price cannot be negative so Cost Price was Rs. 30.
ANSWER : OPTION D
Answer: (D) 30
Question: 5358 x 53 = ?
(A) 272258
(B) 272358
(C) 283974
(D) 274258
(E) 274358
Rationale: 5358 x 51	= 5358 x (50 + 3)
= 5358 x 50 + 5358 x 3
= 267900 + 16074
= 283974.
C)
Answer: (C) 283974
Question: Sheila works 8 hours per day on Monday, Wednesday and Friday, and 6 hours per day on Tuesday and Thursday. She does not work on Saturday and Sunday. She earns $360 per week. How much does she earn in dollars per hour?
(A) 11
(B) 10
(C) 9
(D) 8
(E) 7
Rationale: Let Sheila earn x dollars per hour
So, on Monday, Wednesday and Friday , she earns 8x each
And, on Tuesday and Thursday, she earns 6x each
In total , over the week she should earn, 3(8x) + 2(6x) = 36x
She earns $360 per week
36x =360
x =10
Correct Option : B
Answer: (B) 10
Question: In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be
worth Rs. 64.50 per Kg?
(A) 1 : 2
(B) 2 : 1
(C) 3 : 1
(D) 1 : 3
(E) None of these
Rationale: Explanation :
By the rule of alligation, we have
Cost of 1 kg of 1st kind tea Cost of 1 kg tea of 2nd kind tea
62 72
Mean Price
64.5
72-64.5=7.5 64.5-62=2.5
Required Ratio = 7.5 : 2.5 = 3 : 1
Answer : Option C
Answer: (C) 3 : 1
Question: An investor can sell her MicroTron stock for 36$ per share and her Dynaco stock for 60$ per share, If she sells 300 shares altogether, some of each stock, at an average price per share of 40$, how many shares of Dynaco stock has she sold?
(A) 50
(B) 75
(C) 92
(D) 136
(E) 184
Rationale: w1/w2 = (A2 - Aavg)/(Aavg - A1) = (60 - 40)/(40 - 36) = 20/4 = 5/1 = Number of MicroTron stocks/Number of Dynaco stocks
So for every 5 MicroTron stock, she sold 1 Dynaco stock.
So out of 300 total stocks, (1/5)th i.e. 300/6 = 50 must be Dynaco stock.
Answer (A)
Answer: (A) 50
Question: A box contains four copper coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
(A) 3/4
(B) 1/5
(C) 2/5
(D) 3/5
(E) 4/5
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = 4/5
Option E
Answer: (E) 4/5
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 6 different boat to go and 4 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 40
(C) 45
(D) 60
(E) 24
Rationale: Ans.(E)
Sol. Number of choices to go by ship = 6 Number of choices to return by airline = 4 From, fundamental principle, total number of ways of performing the journey = 6 x 4 = 24 ways
Answer: (E) 24
Question: Gold is 19 times as heavy as water and copper is 9 times as heavy as water. In what ratio should these be mixed to get an alloy 13 times as heavy as water?
(A) 1:2
(B) 2:3
(C) 4:1
(D) 5:2
(E) 6:5
Rationale: G = 19W
C = 9W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
19W+9Wx = x+1 * 13W
19+9x = 13(x+1)
x = 3/2
Ratio of gold with copper = 1:3/2 = 2:3
Answer is B
Answer: (B) 2:3
Question: A certain debt will be paid in 40 installments from January 1 to December 31 of a certain year. Each of the first 20 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 20 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
(A) 442.5
(B) 450
(C) 465
(D) 468
(E) 475
Rationale: Total number of installments = 40
Payment per installment for the first 20 installments = 410
Payment per installment for the remaining 20 installments = 410+65=475
Average = (20*410 + 20*475)/40 =442.50
Answer A
Answer: (A) 442.5
Question: Paul sells encyclopedias door-to-door. He earns $80 on every paycheck, regardless of how many sets he sells. In addition, he earns commission as follows:
Commission Sales
10% $0.00 - $10,000.00
5% $10,000.01 --->
He does not earn double commission.That is, if his sales are $12,000, he earns 10% on the first $10,000 and 5% on the remaining $2,000.
His largest paycheck of the year was $1,320. What were his sales for that pay period?
(A) 13,200
(B) 14,800
(C) 16,400
(D) 15,800
(E) 19,600
Rationale: His pay check was $1320.
Out of this, $80 was his fixed salary so the total commission he earned was $1320 - $80 = $1240
He earns 10% on the sales of first $10,000 which gives a commission of $1000.
He earns 5% on every subsequent dollar. Since he earns another $240, he must have had sales of another 240*(100/5) = 4800
So his total sales must have been $10,000 + $4800 = $14,800
B
Answer: (B) 14,800
Question: A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9% p.a. in 5 years. What is the sum?
(A) 2762
(B) 2877
(C) 2882
(D) 8925
(E) 2887
Rationale: Principal = (100 * 4016.25) / (9 * 5)
= Rs.8925.
Answer:D
Answer: (D) 8925
Question: Two right circular cylinders of equal volumes have their heights in the ratio 1:2. Find the ratio of their radii.
(A) √2:6
(B) √2:1
(C) √2:1
(D) √2:2
(E) √2:4
Rationale: Let their heights be h and 2h and radii be r and R respectively then.
πr2h=πR2(2h)=>r2R2=2hh=21=>rR=2–√1=>r:R=√2:1
Answer:C
Answer: (C) √2:1
Question: The average of 11 numbers is 10.9. If the average of first six is 10.5 and that of the last six is 11.4 the sixth number is?
(A) 11.9
(B) 11.4
(C) 11.2
(D) 11.5
(E) 11.1
Rationale: 1 to 11 = 11 * 10.9 = 119.9
1 to 6 = 6 * 10.5 = 63
6 to 11 = 6 * 11.4 = 68.4
63 + 68.4 = 131.4 – 119.9 = 11.5
6th number = 11.5
Answer:D
Answer: (D) 11.5
Question: If the price of gold increases by 40%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?
(A) 331/8%
(B) 26.67%
(C) 28.5%
(D) 332/3%
(E) 131/3%
Rationale: 100
140
------
140-------40
100-------? => 28.5%
Answer:C
Answer: (C) 28.5%
Question: In a school where there are more than 100 students when they are grouped into 12 and 16, always 6 students remain ungrouped. What would be the minimum number of new students to be registered to this school such that when they are grouped into 20 then none of the stundents remains ungrouped ?
(A) 6
(B) 8
(C) 9
(D) 10
(E) 12
Rationale: S=12a+6=16b+6
6a = 8b --> for S>100 min(a,b) = (12,9)
then number of stundent in school --> 12*12 +6 = 150
20k = 150 + x so that none will be ungrouped --> min( k) = 8 then
20*8 =150 + x
x = 10 new students to be registered
ANSWER: D
Answer: (D) 10
Question: A, B and C started a shop by investing Rs. 5,000, Rs. 15,000 and Rs. 30,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 3000, then the total profit was :
(A) 30,000
(B) 5,000
(C) 80,000
(D) 120,000
(E) None
Rationale: Sol.
A : B : C = 5000 : 15000 : 30000 = 1: 3 : 6. so, Câ€™s share : Total Profit = 6 : 10
Let the total profit be Rs. x. Then, 6/10 = 3000/x or x
= 3000 * 10 /6 = 5000.
Answer B
Answer: (B) 5,000
Question: Two equally sized jugs full of water are each emptied into two separate unequally sized empty jugs, X and Y. Now, jug X is 1/6 full, while jug Y is 2/3 full. If water is poured from jug X into jug Y until jug Y is filled, what fraction of jug X then contains water?
(A) 0
(B) 1/12
(C) 2/15
(D) 1/10
(E) 2/10
Rationale: Suppose the water in each jug is L liters
CX x (1/6) = L
CX = 6L liters
CX is capacity of X
CY x (2/3) = L
CY = 3L/2 liters
CY is capacity of Y
Now, Y is 3L/2 - L empty = L/2 empty
So, we can put only L/2 water in jug Y from Jug X
Jug X's remaining water = L - L/2 = L/2
Fraction of X which contains water = water / CX
= (L/2)/ 6L
= 1/12
Answer will be B
Answer: (B) 1/12
Question: In a apartment, 30% of the people speak English, 20% speak Hindi and 11% speak both. If a people is selected at random, what is the probability that he has speak English or Hindi?
(A) 1/30
(B) 12/13
(C) 16/41
(D) 12/91
(E) 13/71
Rationale: P (E) = 30 / 100 , P (H) = 20 / 100 and P (E âˆ© H) = 11 / 100 =
P (E or H) = P (E U H)
= P (E) + P (H) - P (E âˆ© H)
= (30 / 100) + (20/100 - (11 / 100) = 39/100 = 16/41
C
Answer: (C) 16/41
Question: A satellite is composed of 24 modular units, each of which is equipped with a set of sensors, some of which have been upgraded. Each unit contains the same number of non-upgraded sensors. If the number of non-upgraded sensors on one unit is 1/3 the total number of upgraded sensors on the entire satellite, what fraction of the sensors on the satellite have been upgraded?
(A) 5/6
(B) 1/5
(C) 1/6
(D) 1/9
(E) 1/24
Rationale: Let x be the number of upgraded sensors on the satellite.
The number of non-upgraded sensors per unit is x/3.
The number of non-upgraded sensors on the whole satellite is 24(x/3) = 8x.
The fraction of sensors which have been upgraded is x / (x+8x) = x/9x = 1/9
The answer is D.
Answer: (D) 1/9
Question: Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 44 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
(A) 140 sec
(B) 132 sec
(C) 192 sec
(D) 252 sec
(E) None
Rationale: Solution
Relative Speed	= (44 - 40 ) Kmph
= 4 kmph
=(4 x 5 / 18)m/sec
= (20 / 18 ) m/sec
Time taken	= (350 x 18 / 20) sec
= 140 sec.
Answer A
Answer: (A) 140 sec
Question: Boy sells a book for Rs. 450 he gets a loss of 10 %, To gain 10 %, what should be the SP?
(A) Rs.330
(B) Rs.430
(C) Rs.550
(D) Rs.600
(E) Rs.620
Rationale: Find Selling Price to gain 10 %.
Now, we are asked to find selling price to gain 10% profit.
Hint:
Selling Price = (100 + Gain%) × C.P.
100
Selling Price = (100 + 10) × 500
100
Selling Price = (110) × 500
100
Therefore, selling Price = Rs.550
C
Answer: (C) Rs.550
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 4
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: (B) 8
Question: The average of runs of a cricket player of 20 innings was 32. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
(A) 96
(B) 106
(C) 122
(D) 116
(E) 122
Rationale: Average = total runs / no.of innings = 32
So, total = Average x no.of innings = 32 * 20 = 640
Now increase in avg = 4 runs. So, new avg = 32+4 = 36 runs
Total runs = new avg x new no. of innings = 36 * 21 = 756
Runs made in the 11th inning = 756-640 = 116
ANSWER:D
Answer: (D) 116