mathewhe/aqua_rat huggingface dataset:
Question: A and B together can do a work in 4 days. If A alone can do it in 20 days. In how many days can B alone do it?
(A) 11
(B) 5
(C) 6
(D) 8
(E) 25
Rationale: B
5
1/4 â€“ 1/20 = 1/5 => 5
Answer: (B) 5
Question: If a and b are positive integers and a/b=0 then which of the following give positive Numbers and CANNOT be zero?
(A) ab/ba
(B) a/b-b/a
(C) b/a-a/b
(D) (a^2 -b^2)/ab
(E) a/b
Rationale: (D) (a^2 -b^2)/ab = a/b-b/a gives negative value.
The option C is Answer.
(C)a/b-b/a
If a/b=0, b/a gives positive numbers.(a and b are positive integers)
Answer: (C) b/a-a/b
Question: For which of the following values of s is (30+s)/s an integer?
(A) 3
(B) 4
(C) 9
(D) 11
(E) 30
Rationale: This problem has to be solved by checking the options
(30 + s)/s
For this entity to be an integer, 50 + s should be divisible by s
Option A:33/3 - Not an Integer
Option B: 34/4 - Not an Integer
Option C: 39/9 - Not an integer
Option D: 41/11 - Not an integer
Option E - 60/30 - Integer
Correct Option: E
Answer: (E) 30
Question: In the decimal notation of number (223)3(223)3, what is the third digit to the right of the decimal point?
(A) 0
(B) 1
(C) 2
(D) 4
(E) 8
Rationale: Because (2/23)3<(2/20)3=(1/10)3=0.001, the third digit to the right of the decimal point in the decimal notation of (2/23)3 is 0.
Answer: A
Answer: (A) 0
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 2500. The difference between the profit shares of A and C is?
(A) 621
(B) 276
(C) 236
(D) 1000
(E) 211
Rationale: Explanation:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 2500
=> 5 parts out of 15 parts is Rs. 2500
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (2500) = Rs. 1000
Answer: D
Answer: (D) 1000
Question: If 15% of A is the same as 40% of B, then A : B is :
(A) 5:4
(B) 8:3
(C) 7:16
(D) 2:17
(E) 3:5
Rationale: Expl : 15% of A I= 40 % of B =15A/100 = 40B/100 = 8/3 = 8:3
Answer:B
Answer: (B) 8:3
Question: If y exceeds x by 20%, then x is less than y by?
(A) 16 8/3%
(B) 16 9/3%
(C) 16 2/3%
(D) 16 2/9%
(E) 13 2/3%
Rationale: X=100	y=120
120------20
100-------? => 16 2/3%
Answer:C
Answer: (C) 16 2/3%
Question: A train crosses a platform of 120 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150
(B) 88
(C) 270
(D) 62
(E) 52
Rationale: Length of the train be â€˜Xâ€™
X + 120/15 = X + 250/20
4X + 480 = 3X + 750
X = 270m
Answer: C
Answer: (C) 270
Question: A shopkeeper offers 2.5% discount on cash purchases. What cash amount would Rohan pay for a cycle the marked price of which is $650?
(A) $523.89
(B) $600.25
(C) $710.45
(D) $690.63
(E) $633.75
Rationale: S.P. = 97 1/2% of $650 = 195/2 * 1/100 * 650 = $633.75
Answer is E
Answer: (E) $633.75
Question: z is a positive integer and multiple of 2; v = 4^z, what is the remainder when v is divided by 10?
(A) 10
(B) 6
(C) 4
(D) 0
(E) It Cannot Be Determined
Rationale: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:
4/10 is 0 with a remainder of 4
14/10 is 1 with a remainder of 4
5/10 is 0 with a remainder of 5
105/10 is 10 with a remainder of 5
It is also essential to remember that the z is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, z must be a positive even integer.
With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?
The units digit of 4 raised to an integer follows a specific repeating pattern:
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^(odd number) --> units digit of 4
4^(even number) --> units digit of 6
There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.
Since z must be an even integer, the units digit of v=4^z will always be 6. Consequently, the remainder when v=4^z is divided by 10 will always be 6.
In case this is too theoretical, consider the following examples:
z=2 --> v=4^z=16 --> v/10 = 1 with a remainder of 6
z=4 --> v=4^z=256 --> v/10 = 25 with a remainder of 6
z=6 --> v=4^z=4096 --> v/10 = 409 with a remainder of 6
z=8 --> v=4^z=65536 --> v/10 = 6553 with a remainder of 6
Answer: B.
Answer: (B) 6
Question: The CI on Rs. 30,000 at 7% per year is Rs. 4347. The period is?
(A) 1 year
(B) 2 years
(C) 3 years
(D) 4 years
(E) 5 years
Rationale: Amount = Rs. (30000 + 4347) = Rs. 34347.
Let the time be n years.
Then, 30000 1 +	7 n	= 34347
100
107 n	=	34347	=	11449	= 107 2
100	30000	10000	100
n = 2 years
B
Answer: (B) 2 years
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 37 km/hr
(B) 50 km/hr
(C) 36 km/hr
(D) 26 km/hr
(E) 87 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 5 = 45 => x = 50 km/hr.
Answer:B
Answer: (B) 50 km/hr
Question: A committee is reviewing a total of 20x black-and-white films and 6y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction R of the selected films are in color?
(A) 1/130
(B) 1/5
(C) 3/13
(D) 10/13
(E) 30/31
Rationale: It's y/xpercentnot y/x.
If x=20 and y=10. Then:
20x=400 black-and-white films;
6y=60 color films.
y/x%=10/20%=0.5% of the black-and-white films, so 2 black-and-white films and all 60 color films, thus total of 62 films were selected.
Color films thus compose R=60/62=30/31 of the selected films.
Answer: E.
Answer: (E) 30/31
Question: The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water?
(A) 2
(B) 7
(C) 5
(D) 4
(E) 8
Rationale: S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4)
= 2
x = 8
Answer: E
Answer: (E) 8
Question: Find Next Number in the Series
2 9 3 1 8 4 3 6 5 7 ?
(A) 6
(B) 8
(C) 10
(D) 11
(E) 2
Rationale: E
2
This single sequence in fact consists of two Series:
The first Series is 2-3-4-5-...
and
The second Series is 9-18-36-72-... .
Answer: (E) 2
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
(A) 11
(B) 12
(C) 77
(D) 88
(E) 91
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (120 + 120)/20 = 12 sec.Answer: B
Answer: (B) 12
Question: A contractor undertook to do a piece of work in 9 days. He employed certain number of laboures but 6 of them were absent from the very first day and the rest could finish the work in only 15 days. Find the number of men originally employed .
(A) 15
(B) 6
(C) 13
(D) 9
(E) None of these
Rationale: Let the number of men originally employed be x.
9x = 15(x – 6)
or x = 15
Answer A
Answer: (A) 15
Question: If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is ?
(A) 1/5
(B) 1/2
(C) 1/9
(D) 1/8
(E) 1/2
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer: B
Answer: (B) 1/2
Question: 10 speakers gathered to deliver speeches on two topics. Even though 10 speeches were initially planned to be delivered, due to lack of time only 2 speeches were finally decided to be delivered. Topics are to be spoken in a specific order and the speeches differ with respect to speaker or topic. How many such two speeches are possible?
(A) 2
(B) 20
(C) 50
(D) 100
(E) 1024
Rationale: 1)there are 10 speeches in ONE topic and 10 in OTHER..
2)there is a specific order for topics, so
a) both the topics are to be spoken on- so ONE from each
b) the order does not matter since there is ONLY one specific order..
so 10C1∗10C1=10∗10=100
ANSWER:D
Answer: (D) 100
Question: In how many ways can 4 indistinguishable red balls and 2 different blue balls be arranged in a line?
(A) 6!
(B) 30
(C) 40
(D) 6!/2!
(E) 4!/2!
Rationale: The total number of ways in which a total N items, out of which p are identical of one type, q are identical of another type and rest are different, can be arranged in a line is N!/{p!q!}
In the given problem, we have 6 balls out of which 4 are identical.
Hence the number of arrangements possible are 6!/4! = 30
Ans B
Answer: (B) 30
Question: To be eligible for retirement benefits at the Sieman Corporation, the sum of an employee's age, in years, and the number of years employment must be at least 64. If x, where x <64, is a certain employee's age when hired and y is the minimum number of years of employment required for the employee to be eligible for retirement benefits, which of the following equations represents the relationship between x and y?
(A) x+2y=64
(B) xy=64
(C) 2x+y=64
(D) x+y=64
(E) 2x+2y=64
Rationale: We are told that when a certain employee was hired he was x years old and that the he needed minimum y years to be eligible for benefits.
Now,after y years of employment, when the employee will be be eligible for benefits, the employee will be x+y years old and will have y years of employment, thus{age after y years}+{employment years}=(x+y)+y=x+2y=64.
Answer: A
Answer: (A) x+2y=64
Question: Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants?
(A) 126
(B) 120
(C) 101
(D) 112
(E) 115
Rationale: 8 shirts
9 pants
we can combine 2 shirts with (12-3) pants
2*9=18
we can combine the other shirts (6) with any pants (9)
9*12=54
Thus total :108+18=126	ANS:A
Answer: (A) 126
Question: In the first 20 overs of a cricket game, the run rate was only 4.2. What should be the run rate in the remaining 30 Overs to reach the target of 324 runs?
(A) 7.25
(B) 8.5
(C) 8
(D) 9.15
(E) 10
Rationale: Explanation :
Required run rate = (324 - 4.2 20 ) = 240/ 30 = 8.
Answer : C
Answer: (C) 8
Question: The average weight of 8 person's increases by 4.2 kg when a new person comes in place of one of them weighing 65 kg. What is the weight of the new person?
(A) 75 Kg
(B) 50 Kg
(C) 85 Kg
(D) 80 Kg
(E) 98.6 KG
Rationale: Explanation:
Total increase in weight = 8 Ã— 4.2 = 33.6
If x is the weight of the new person, total increase in weight = xâˆ’65
=> 33.6 = x - 65
=> x = 33.6 + 65 = 98.6
Answer: Option E
Answer: (E) 98.6 KG
Question: In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
(A) 25
(B) 40
(C) 35
(D) 60
(E) 55
Rationale: The first letter can be posted in any of the 3 post boxes. Therefore, we have 3 possibilities.
Similarly, the second, the third, the fourth and the fifth letter can each be posted in any of the 3 post boxes.
Each of the 5 letters has 3 possibilities because we can post any number of letters in all of the boxes.
Therefore, the total number of ways the 5 letters can be posted in 3 boxes is
3 * 3 * 3 * 3 * 3 = 35
Ans: C
Answer: (C) 35
Question: A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively.The length of the train is:
(A) 35M
(B) 45M
(C) 55M
(D) 50M
(E) 40M
Rationale: 2 kmph = ( 2 x 5/18) m/sec = 5/9 m/sec.
4 kmph = ( 4 x 5/18)m/sec = 10/9 m/sec.
Let the length of the train be x metres and its speed by y m/sec.
Then, ( x / y-5) = 9 and x / (y-10/ 9) = 10.
Therefore 9y - 5 = x and 10(9y - 10) = 9x
=9y - x = 5 and 90y - 9x = 100.
On solving, we get: x = 50 ANSWER : D
Answer: (D) 50M
Question: A movie buff owns movies on DVD and on Blu-ray in a ratio of 9:2. If she buys 2 more Blu-ray movies, that ratio would change to 17:4. If she owns movies on no other medium, what was the original number of movies in her library before the extra purchase?
(A) 22
(B) 28
(C) 77
(D) 99
(E) 187
Rationale: if u can just keep an eye on the options
99 is the only multiple of 9 in options given .. SO you can mark it wid in seconds.
Now coming to the process m(D) = 9x and b(D) = 2x
now from the next line the new eqn becomes 9x/ (2x + 2) = 17/4
Solving it 36x = 34x + 34x =17
which means m (d) = 153 and b(d) = 34
SO total initially is m(d) + b(d) = 187
E
Answer: (E) 187
Question: Two bus tickets from city A to B and three tickets from city A to C cost Rs. 385 but three tickets from city A to B and two tickets from city A to C cost Rs. 365. What are the fares for cities B and C from A ?
(A) s. 4, Rs. 23
(B) s. 13, Rs. 17
(C) s. 15, Rs. 14
(D) s. 17, Rs. 13
(E) s. 65, Rs. 85
Rationale: If fares for cities B and C from A are x and y respectively, then
2x+3y=385 or 6x+9y= 1155
3x+2y =365 or 6x+4y= 730
subtracting
5y = 425
y= Rs 85
Hence E. Rs. 65, Rs. 85
ANSWER:E
Answer: (E) s. 65, Rs. 85
Question: 36, 34, 30, 28, 24, 22, 18, 16, ?
(A) 12
(B) 10
(C) 8
(D) 6
(E) 4
Rationale: This is an alternating number subtraction series. The pattern is -2, -4, -2, ....
The answer is A.
Answer: (A) 12
Question: A and B started a partnership business investing Rs. 20,000 and Rs. 15,000 respectively. C joined them with Rs. 20,000 After six months. Calculate B's share in total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
(A) 7500
(B) 8500
(C) 9000
(D) 8000
(E) None of these
Rationale: Explanation :
A : B : C = 20000*24 : 15000*24 : 20000*18 = 20*4 : 15*4 : 20*3
= 4*4 : 3*4 : 4*3
= 4:3:3
B's Share = 25000 * 3/10 = 7500. Answer : Option A
Answer: (A) 7500
Question: There were two candidates in an election. Winner candidate received 54% of votes and won the election by 288 votes. Find the number of votes casted to the winning candidate?
(A) 776
(B) 1944
(C) 2199
(D) 2157
(E) 2125
Rationale: W = 54% L = 46%
54% - 46% = 8%
8% -------- 288
54% -------- ? => 1944
Answer:B
Answer: (B) 1944
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 400 m long?
(A) 266 Sec
(B) 160 Sec
(C) 776 Sec
(D) 166 Sec
(E) 997 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1600 m
T = D/S
T = 1600/10
T = 160 Sec
Answer: B
Answer: (B) 160 Sec
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
(A) 3/98
(B) 2/28
(C) 2/21
(D) 2/29
(E) 2/24
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles. Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 * 2)/(15 * 14) = 1/35
Probability that both are yellow = ²C₂/¹⁵C₂ = (2 * 1)/(15 * 14) = 1/105
Probability that one blue and other is yellow = (³C₁ * ²C₁)/¹⁵C₂ = (2 * 3 * 2)/(15 * 14) = 2/35
Required probability = 1/35 + 1/105 + 2/35
= 3/35 + 1/105 = 1/35(3 + 1/3)
= 10/(3 * 35) = 2/21
Answer:C
Answer: (C) 2/21
Question: How many numbers can be made with digits 0, 7, 8 which are greater than 0 and less than a million?
(A) 496
(B) 486
(C) 1084
(D) 728
(E) 628
Rationale: The number of single digit numbers = 2
The number of 2 digit numbers = 2 × 3 = 6
The number of 3 digit numbers = 2 × 3 × 3 = 18
The number of 4 digit numbers = 2 × 3 × 3 × 3 = 54
The number of 5 digit numbers = 2 × 3 × 3 × 3 × 3 = 162
The number of 6 digit numbers = 2 × 3 × 3 × 3 × 3 × 3 = 486
Therefore, the total numbers = 728
ANSWER:D
Answer: (D) 728
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
(A) 10 / 21
(B) 11 / 21
(C) 2 / 7
(D) 5 / 7
(E) 6 / 7
Rationale: Total number of balls = (2 + 3 + 2) = 7.
Let S be the sample space.
Then, n(S)	= Number of ways of drawing 2 balls out of 7
= 7C2 `
=(7 x 6)/(2 x 1)
= 21.
Let E = Event of drawing 2 balls, none of which is blue.
n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.= 5C2 =	(5 x 4)/(2 x 1) = 10.
P(E) =	n(E)/n(S)	=	10/21
Answer: A.
Answer: (A) 10 / 21
Question: There are 750 male and female participants in a meeting. Half the female participants and one-quarter of the male participants are Democrats. One-third of all the participants are Democrats. How many of the Democrats are female?
(A) 150
(B) 135
(C) 160
(D) 125
(E) None
Rationale: Explanation :
Let m be the number of male participants and f be the number of female articipants in the meeting.
Thetotal number of participants is given as 750.
Hence, we have m+f= 750
Now, we have that half the female participants and one-quarter of the male participants are
Democrats.
Let d equal the number of the Democrats.
Then we have the equation f/2 + m/4 =d
Now, we have that one-third of the total participants are Democrats. Hence, we have the equation
=> d = 750/3 = 250
Solving the three equations yields the solution
=> f = 250,m= 500, and d= 250.
The number of female democratic participants equals half the female participants equals
=> 250/2 = 125.
Hence (D) is the correct answer.
Answer : D
Answer: (D) 125
Question: On the first day of her vacation, Louisa traveled 100 miles. On the second day, traveling at the same average speed, she traveled 175 miles. If the 100-mile trip took 3 hours less than the 175-mile trip, what was the average speed, in miles per hour?
(A) 27
(B) 28
(C) 25
(D) 30
(E) 35
Rationale: (time)*(rate) = (distance)-->(rate) = (distance)/(time)--> given:(rate) = 100/t = 175/(t+3)-->4/t = 7/(t+3)-->4t+12=7t ---->3t= 12 . t= 4 ---->(rate ) = 100/4 = 25
Answer: C
Answer: (C) 25
Question: The instructions state that Cheryl needs 5/11 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 25/55 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) 1 2/3
(D) 2/3
(E) 2 1/9
Rationale: total bought = 5/11+2/3
left part 25/55--->5/11
so used part 5/11+2/3-5/11=2/3
Ans D
Answer: (D) 2/3
Question: A shopkeeper sells his goods at cost price but uses a faulty meter that weighs 990 grams. Find the profit percent.
(A) 1.05
(B) 1.06
(C) 1.01
(D) 1.08
(E) 1.09
Rationale: Explanation:
(100 + g) / (100 + x) = True measure / Faulty measure
x = 0
true measure = 1000
faulty measure = 990
100 + g / 100 + 0 = 1000 / 990
100+g = 100/99*100
g = 1.01
ANSWER: C
Answer: (C) 1.01
Question: In the recent, science conference in New York, out of 400 men, 1100 women, 300 children present inside the building premises, 40% of the men, 30% of the women and 20% of the children were Indians. Find the percentage of people who were Indian?
(A) 37.22%
(B) 28.66%
(C) 34.55%
(D) 33.55%
(E) 30.55%
Rationale: Solution: Number of Indians men present there = 400*40/100 = 160
Indian women = 1100*30/100 = 330
Indian children = 300*20/100 = 60.
Total member present in science conference = 400+1100+300=1800
Total Indian = 160+330+60 = 550
Hence, % of Indian present there = 550*100/1800 = 30.55%
Answer E
Answer: (E) 30.55%
Question: At what rate percent on simple interest will Rs.750 amount to Rs.900 in 5 years?
(A) 9%
(B) 6%
(C) 4%
(D) 2%
(E) 1%
Rationale: 150 = (750*5*R)/100
R = 4%
Answer: C
Answer: (C) 4%
Question: On a purchase of $127, a store offered a payment plan consisting of a $27 down payment and 12 monthly payments of $10 each. What percent of the purchase price, to the nearest tenth of a percent, did the customer pay in interest by using this plan?
(A) 18.3%
(B) 15.3%
(C) 21.3%
(D) 22.3%
(E) 25.3%
Rationale: 12*10 + 27 = 147
(27/127)* 100 = 21.3
Answer : C
Answer: (C) 21.3%
Question: A rectangular grassy plot 110m by 65cm has a gravel path .5cm wide all round it on the inside. Find the cost of gravelling the path at 80 paise per sq.mt?
(A) 680rs
(B) 540rs
(C) 480rs
(D) 640rs
(E) 280rs
Rationale: area of theplot = 110 * 65 = 7150 sq m
area of the plot excluding the path = (110-5)* (65-5) = 6300 sq m
area of the path = 7150 - 6300 =850 sq m
cost of gravelling the path = 850 * 80/100 = 680 Rs
Answer: A
Answer: (A) 680rs
Question: A man took a loan at rate of 12% per annum simple interest. After 3 years he had to pay 4320 interest. The principal amount borrowed by him was.
(A) Rs 14000
(B) Rs 15000
(C) Rs 12000
(D) Rs 17000
(E) None of these
Rationale: Explanation:
S.I.=Pâˆ—Râˆ—T/100
=>P=S.I.âˆ—100/Râˆ—T
=>P=4320âˆ—100/12âˆ—3=Rs12000
Option C
Answer: (C) Rs 12000
Question: Walking 7/6 of his usual rate, a boy reaches his school 3 min early. Find his usual time to reach the school?
(A) 21
(B) 28
(C) 99
(D) 77
(E) 66
Rationale: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
3 --------- ?
= 21 m
Answer:A
Answer: (A) 21
Question: Machines X and Y produce bottles at their respective constant rates. Machine X produces k bottles in 4 hours and machine Y produces k bottles in 5 hours. How many hours does it take machines X and Y , working simultaneously , to produce 10k bottles?
(A)  8 2/3
(B)  12 5/3
(C)  15
(D)  18
(E)  22 2/9
Rationale: x rate = k/4
y rate = k/5
k/4 + k/5 = 10k / T
solving T = 200/9 = 22 (2/9)
Answer E
Answer: (E)  22 2/9
Question: How many pairs of letters are there in the word INSTITUTE which have as many letters between them in the word as in the English alphabet?
(A) 6
(B) 2
(C) 1
(D) 3
(E) 7
Rationale: N _ _ _ _ _T
ST
TU
so total= 3
ANSWER:D
Answer: (D) 3
Question: P, Q and R can do a work in 6 , 9 and 12 days respectively. They completed the work and got Rs.195. What is the share of P?
(A) 80
(B) 70
(C) 85
(D) 90
(E) 95
Rationale: The ratio of their working rates = 1/6 : 1/9 : 1/12 = 6 : 4 : 3.
Since, they work together, the share of P
= 6/13 * 195 = Rs.90
Answer: D
Answer: (D) 90
Question: A table is bought for Rs.500/- and sold at Rs.600/- find gain or loss percentage
(A) 25% gain
(B) 20% gain
(C) 20% loss
(D) 15% gain
(E) None
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (600 - 500)/500 = 20% gain
B
Answer: (B) 20% gain
Question: There are 10 women and 9 men in a certain club. If the club is to select a committee of 2 women and 2 men, how many different such committees are possible?
(A) 1620
(B) 1820
(C) 2060
(D) 2440
(E) 2680
Rationale: 10C2 * 9C2 = 45*36 = 1620
The answer is A.
Answer: (A) 1620
Question: How many odd integers S between 200 and 600 are there such that their tens digit is even?
(A) 20
(B) 25
(C) 100
(D) 150
(E) 200
Rationale: The hundreds digit can take 4 values: 2, 3, 4 and 5;
The tens digit can take 5 values: 0, 2, 4, 6 and 8;
The units digit can take 5 values: 1, 3, 5, 7 and 9;
Total S: 4*5*5=100.
Answer: C.
Answer: (C) 100
Question: A bus takes 2 hours to cover a distance of 180 Km. how much should the speed in Kmph be maintained to cover the same direction in 5/2th of the previous time?
(A) 50 Kmph
(B) 60 Kmph
(C) 36 Kmph
(D) 25 Kmph
(E) 70 Kmph
Rationale: Time = 2
Distance = 180
5/2 of 2 hours = 2 * 5/2 = 5 Hours
Required speed = 180/5 = 36 Kmph
C
Answer: (C) 36 Kmph
Question: The L.C.M. of 2 numbers is 100. The numbers are in the ratio 4:1. Find their product?
(A) 1200
(B) 2000
(C) 2500
(D) 3200
(E) 1250
Rationale: Let the numbers be 4x and x
L.C.M. = 4x
4x = 100
x = 25
The numbers are = 100 and 25
Required product = 100*25 = 2500
Answer is C
Answer: (C) 2500
Question: A 14% stock yielding 10% is quoted at :
(A) 83.33
(B) 110
(C) 112
(D) 140
(E) 160
Rationale: Solution
To earn Rs. 10, money invested = Rs. 100.
To earn Rs. 14, money invested = Rs.(100/10X14) = Rs. 140.
âˆ´ Market value of Rs. 100 stock =Rs. 140
Answer D
Answer: (D) 140