mathewhe/aqua_rat huggingface dataset:
Question: A certain club has exactly 5 new members at the end of its first week. Every subsequent week, each of the previous week's new members (and only these members) brings exactly L new members into the club. If y is the number of new members brought into the club during the twelfth week, which of the following could be y?
(A)  5^1/12
(B)  3^11 * 5^11
(C)  3^12 * 5^12
(D)  3^11 * 5^12
(E)  60^12
Rationale: At the end of the first week, there are 5 new members;
At the end of the second week, there are 5L new members (since each 5 new members from the previous week brings L new members);
At the end of the third week, there are 5L^2 new members (since each 5L new members from the previous week brings L new members);
...
At the end of the twelfth week, there are 5L^11 new members (since each 5L^10 new members from the previous week brings L new members).
We are given that 5L^11=y. Out of the answers only D yields integer value for L: 5L^11=3^11 * 5^12 --> L=3*5=15.
Answer: D.
Answer: (D)  3^11 * 5^12
Question: a' and 'b' are positive integers such that their LCM is 20 and their HCF is 1. What is the addition between the maximum and minimum possible values of 'a - b'?
(A) 0
(B) 12
(C) 24
(D) 26
(E) 18
Rationale: possible values of a and b can be 5,4; 4,5 and 1,20; 20,1
maximum possible value for a-b is 20-1=19
minimum possible value for a-b is 1-20=-19
19-19=0 ans is A
Answer: (A) 0
Question: A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train?
(A) 28
(B) 27
(C) 299
(D) 277
(E) 150
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer: E
Answer: (E) 150
Question: A book club rented the party room of a local restaurant to meet and discuss its current novel over dinner. The total charge, including food and service, was $ 950. If each member of the club paid at least $ 42, then what is the greatest possible number of members in the club?
(A) 19
(B) 20
(C) 21
(D) 25
(E) 23
Rationale: Given: Each person spends $42.
By looking at the options, we see that if there were 20 members, each person will spend atleast $42.
Hence the greatest number of members = 22.6. Option E
Answer: (E) 23
Question: what is the value of (4)^-6 ?
(A) 1/1008
(B) 1/6400
(C) 1/6550
(D) 1/6660
(E) 1/4096
Rationale: 4^-6= 1/(4)^6= 1/4096
ANSWER:E
Answer: (E) 1/4096
Question: Set B consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set B?
(A) 6
(B) 4
(C) 1
(D) 7
(E) 76
Rationale: Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).
Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....
Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...
Putting the 7 numbers in order, we have:
-27, -3, -2, 2, 3, 15, 17
This means that the2will either be the 4th term or the 5th term (depending on the value of N).
IF....
N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5
N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0
Neither of those answers is among the choices though, so N must be something relativelycloseto 2.....
IF....
N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.
C
Answer: (C) 1
Question: A baker filled with a measuring cup with a cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
(A) 1/8 cup
(B) 3/8 cup
(C) 1/4 cup
(D) 1/2 cup
(E) 9/8 cup
Rationale: 3/4 is the original water in cup .half in batter.So left is 3/8 out which 1/8 is spilled out.So again left with 2/8.
so 50% more than what he started was = 8/8+1/2*(3/4)=11/8
Amount of water needed to add = 11/8 - 2/8=9/8
ANSWER:E
Answer: (E) 9/8 cup
Question: One thief entered a cave where he found a pile of diamonds. At first he thought of taking all. But listening to his conscience he thought of taking only half of them. But while returning he picked up two more from the pile. After that Second thief entered the cave and bagged half of remaining diamonds and picked up two more while returning. Later third thief entered and did the same. Even the fourth thief did the same. When the fifth thief entered he found only one diamond in the cave. How many diamonds are there in the cave at first.
(A) 74
(B) 75
(C) 76
(D) 77
(E) 78
Rationale: When 5th thief entered-1 diamond
When 4th thief entered -(1+2)*2=6 diamonds
When 3rd thief entered -(6+2)*2=16 diamonds
When 2nd thief entered -(16+2)*2=36 diamonds
When 1st thief entered -(36+2)*2=76 diamonds
ANSWER:C
Answer: (C) 76
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 8 m of the same rod?
(A) 22.8 kg
(B) 25.6 kg
(C) 28 kg
(D) 30.4 kg
(E) None of these
Rationale: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 8 :: 42.75 : x
=> 11.25 x x = 8 x 42.75
=> x = (8 x 42.75) / 11.25
=> x = 30.4
Answer : D
Answer: (D) 30.4 kg
Question: A set of 13 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
(A) 32
(B) 37
(C) 40
(D) 43
(E) 41
Rationale: The correct answer is E.
A set of 13 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
Given 15 different integers, lets say
n1, n2, n3, n4, n5, n6, n7, n8, n9, n10, n11, n12, n13, n14, n15
Also given median is 25 i.e. n8 = 25
n1, n2, n3, n4, n5, n6, n7, 25, n9, n10, n11, n12, n13, n14, n15
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
18, 19, 20, 21, 22, 23, 24, 25, n9, n10, n11, n12, n13, n14, n15
Also given the range is 25 i.e. n15 - n1 (18) = 23
The maximum value n15 can have is 23+ n1 (18) = 41
E
Answer: (E) 41
Question: Of the 10 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 employees consist of 3 women and one man?
(A) 22
(B) 50
(C) 56
(D) 70
(E) 105
Rationale: another approach :
one scenario : [WWWM]
now we have 5 ways for the first women , 4 ways for the 2nd women and , 3 ways for the third women.
and 5 ways to select one man
so 5*4*3*5 = 300
now the three women are same so combinations with win them are irrelevant the 3 women can we arranged in 3! ways
hence 300/3!= 300/6=50
B
Answer: (B) 50
Question: I had a certain amount of candies with me. I gave half of them with one more to my first son. Then, I gave the remaining half with one more to the younger son. Now I was left with just one candy.
How much candies did I have in the beginning?
(A) 10
(B) 15
(C) 22
(D) 25
(E) 12
Rationale: A
I had 10 candies in the beginning.
Explanation:
Let us take and solve this problem in the reverse direction.
At the end, I was left with 1 candy. Let me take the extra one candy back from my younger son. Now since I gave him half of what I had, we must be having the same number of candies. I have 2, which means he also have 2. This implies that I was left with 4 candies after I gave some to the elder son.
Let me take back the extra candy from my elder son now. Now I have 5 candies. Since I gave him half of what I had, he must be having 5 candies as well. Thus, I had 10 candies in the beginning.
Answer: (A) 10
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) Rs.250
(B) Rs.280
(C) Rs.290
(D) Rs.299
(E) Rs.300
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
A
Answer: (A) Rs.250
Question: Three numbers are in the ratio 3:4:5 and their L.C.M. is 1800. Their H.C.F is?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Let the numbers be 3x,4x and 5x
their L.C.M. = 60x
60x = 1800
x = 30
The numbers are 3*30 , 4*30 , 5*30
Hence required H.C.F. = 30
Answer is B
Answer: (B) 30
Question: There are some pigeons and hares in a zoo. If heads are counted, there are 200. If legs are counted, there are 880. The number of hares in the zoo is?
(A) 90
(B) 99
(C) 77
(D) 66
(E) 240
Rationale: 200*2 = 400
880
-----
480
1----2
?----480 = 240
Answer:E
Answer: (E) 240
Question: A and B complete a work in 3 days. A alone can do it in 9 days. If both together can do the work in how many days?
(A) 3.75 days
(B) 4.75 days
(C) 3.25 days
(D) 3.15 days
(E) 2.75 days
Rationale: 1/3 + 1/9 = 4/9
9/4 = 4.75 days
Answer: B
Answer: (B) 4.75 days
Question: There are 11 cans in the refrigerator. 6 of them are red and 5 of them are blue. In how many ways we can remove 8 cans so that at least one red and at least one blue cans to remain the refrigerator.
(A) 460
(B) 490
(C) 493
(D) 455
(E) 445
Rationale: Answer: E
Answer: (E) 445
Question: What is the probability, to 3 decimal places, that at least two people in a room share the same birthday if there are eleven people in the room? (Assume nobody was born on a leap year)
(A) 0.027
(B) 0.03
(C) 0.076
(D) 0.141
(E) 0.271
Rationale: First, find the probability that nobody has the same birthday: 364/365 * 363/365 * 362/365 * ... * 356/365 * 355/365 = 0.859. Then the correct answer is 1 - 0.859 = 0.141, so the correct answer is D
Answer: (D) 0.141
Question: The average of first 10 natural numbers is?
(A) 5.7
(B) 5.5
(C) 5.4
(D) 5.2
(E) 5.9
Rationale: Sum of 10 natural no. = 110/2
= 55
Average = 55/10
=5.5
Answer: B
Answer: (B) 5.5
Question: A farmer is planting a row consisting of 4 unique apple trees and 5 unique orange trees. How many ways are there for the farmer to plant the trees such that no apple tree is adjacent to another apple tree and no orange tree is adjacent to another orange tree?
(A) 512
(B) 5760
(C) 1,024
(D) 1,152
(E) 10,080
Rationale: 2 possible arrangements are possible
AOAOAOAO
OAOAOAOA
2 unique type of trees are present consisting of 4 trees each
4 apple trees can be arranged in 4! ways
4 orange trees can be arranged in 4! ways
as 2 arrangements are possible
total arrangements = 2 *4! * 5! = 5760
correct answer option B
Answer: (B) 5760
Question: A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely?
(A) 3 hrs 48 min
(B) 3 hrs 45 min
(C) 3 hrs 85 min
(D) 3 hrs 75 min
(E) 3 hrs 25 min
Rationale: Time taken by one tap to fill the tank = 3 hrs.
Part filled by the taps in 1 hour = 4 * 1/6 = 2/3
Remaining part = 1 - 1/2 = 1/2
2/3 : 1/2 :: 1 : x
x = 1/2 * 1 * 3/2 = 3/4 hrs. i.e., 45 min
So, total time taken = 3 hrs 45 min.
Answer: B
Answer: (B) 3 hrs 45 min
Question: A man can row 7 ½ kmph in still water.if in a river running at 1.5 km/hr an hour,it takes him 50 minutes to row to a place and back,how far off is the place?
(A) 1.5 km
(B) 1 km
(C) 2.5km
(D) 2 km
(E) 3 km
Rationale: Speed downstream =(7.5+1.5)km/hr=9 km/hr;
Speed upstream=(7.5-1.5)kmph=6kmph.
Let the required distance be x km.then,
x/9+x/6=50/60.
2x+3x=(5/6*18)
5x=15
x=3.
Hence,the required distance is 3km.
Answer is E.
Answer: (E) 3 km
Question: In an election between two candidates, the winner has a margin of 10% of the votes polled. If 4000 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?
(A) 16000
(B) 10000
(C) 40000
(D) 12000
(E) 5000
Rationale: Winner - Looser
55% - 45%
If 4000 people change their mind and vote for the loser:
Winner - Looser
45% - 55%
Thus 4,000 people compose 25% of all voters, which means that the total number of votes is
40,000
Answer: C
Answer: (C) 40000
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 48 years now, the son's age five years back was:
(A) A)14
(B) B)67
(C) C)19
(D) D)89
(E) E)34
Rationale: Let the son's present age be x years. Then, (48 - x) = x
2x = 48.
x = 24.
Son's age 5 years back (24 - 5) = 19 years.
Answer:C
Answer: (C) C)19
Question: What is the probability for a family with four children to have a girl and three boys (assuming the probability of having a boy or a girl is equal)?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/8
(E) 1/16
Rationale: One possible case is: girl - boy - boy - boy
The probability of this is 1/2*1/2*1/2*1/2 = 1/16
There are 4C3 = 4 such cases so we should multiply by 4.
P(one girl and three boys) = 4/16 = 1/4
The answer is C.
Answer: (C) 1/4
Question: Tom opened a shop investing Rs.3000. Jose joined him 2 months later, investing Rs.4000. They earned a profit of Rs.4230 after completion of one year. What will be Jose's share of profit?
(A) 2000
(B) 2200
(C) 2309
(D) 2350
(E) 3250
Rationale: SoL = ~s- So Anju’s share = [5/9] x 4230 = 2350
D
Answer: (D) 2350
Question: Working alone, Printers X, Y, and Z can do a certain printing job, consisting of a large number of pages, in 12, 40, and 50 hours, respectively. What is the ratio of the time it takes Printer X to do the job, working alone at its rate, to the time it takes Printers Y and Z to do the job, working together at their individual rates?
(A)  4/11
(B)  1/2
(C)  15/22
(D)  200/9
(E)  11/4
Rationale: P1 takes 12 hrs
Rate for P2P3 together = 1/40 + 1/50 = 9/200
Therefore they take 200/9
Ratio = 200/9 = D
Answer: (D)  200/9
Question: If X is to be chosen at random from the integers between 1 to 7, inclusive, and Y is to be chosen at random from the integers between 8 and 12, inclusive, what is the probability that X + Y will be even?
(A) 2/5
(B) 3/7
(C) 5/7
(D) 17/35
(E) 24/35
Rationale: X+Y will be even if X and Y are both even or both odd.
P(X and Y are both even) = 3/7*3/5 = 9/35
P(X and Y are both odd) = 4/7*2/5 = 8/35
P(X+Y is even) = 9/35 + 8/35 = 17/35
The answer is D.
Answer: (D) 17/35
Question: A, B and C can do a piece of work in 24 days, 30 days and 40 days respectively. They began the work together but C left 4 days before the completion of the work. In how many days was the work completed?
(A) 33
(B) 77
(C) 66
(D) 11
(E) 99
Rationale: One day work of A, B and C = 1/24 + 1/30 + 1/40 = 1/10 Work done by A and B together in the last 4 days = 4*(1/24 + 1/30) = 3/10
Remaining work = 7/10
The number of days required for this initial work = 7 days.
The total number of days required = 4 + 7 = 11 days.
Answer:D
Answer: (D) 11
Question: A reduction of 30% in the price of oil enables a house wife to obtain 5kgs more for Rs.800, what is the reduced price for kg?
(A) 46
(B) 47
(C) 48
(D) 49
(E) 50
Rationale: 800*(30/100) = 240 ---- 5
? ---- 1 => Rs.48
Answer: C
Answer: (C) 48
Question: The number of positive integer solutions for the equation x +y +z + t = 30 is
(A) 3854
(B) 3654
(C) 3764
(D) 3960
(E) 4964
Rationale: The number of positive integer solutions for the equatio fx1+x2+⋯+xn=k
(k-1)C(n-1)- where k is the number and n is number of variable in the equation.
30-1 C 4-1 = 29C3 = 3654
Answer : B
Answer: (B) 3654
Question: Michael cashed a check for $1,100 and received only $10 and $50 bills in return. During the course of a day, he used 15 bills and then lost the rest of the money. If the number of $10 bills used was either one more or one less than the number of $50 bills used, what is the minimum possible amount of money that was lost?
(A)  $630
(B)  $800
(C)  $770
(D)  $730
(E)  $700
Rationale: 1. 15 bills spent
2. Number of $10 bills is one more or one less than number of $50 bills.
So, 2 choices
1. 7*10 + 8*50 = $470
2. 8*10 + 7*50 = $430
Least money lost implies most money spent. i.e $470
Therefore, lost money = 1100 - 470 = 630.
Answer A
Answer: (A)  $630
Question: 350 metres long yard, 26 trees are palnted at equal distances, one tree being at each end of the yard. What is the distance between 2consecutive trees
(A) 10
(B) 12
(C) 14
(D) 16
(E) 17
Rationale: 26 trees have 25 gaps between them,
Required distance (350/25) = 14
C
Answer: (C) 14
Question: Working together, Wayne and his son can shovel the entire driveway in three hours. If Wayne can shovel five times as fast as his son can, how many hours would it take for his son to shovel the entire driveway on his own?
(A) 4
(B) 6
(C) 8
(D) 9
(E) 12
Rationale: W: the time for Wyane to do the job
S: the time for his son to do the job
We have 1/W + 1/S = 1/5 and W = 5S
Then we have 1/(5*S) + 1/S = 1/5<=> 6/(5*S) = 1/5 <=> S = 6
ANS: B
Answer: (B) 6
Question: Mrs. B. invested $30,000; part at 5%, and part at 8%. The total interest on the investment was $2,100. How much did she invest at each rate?
(A) x = $1,000, y = $29,000
(B) x = $5,000, y = $25,000.
(C) x = $10,000, y = $20,000.
(D) x = $15,000, y = $15,000
(E) x = $20,000, y = $10,000
Rationale: 2100 = (30000-x) 5/100 + 8x/100
Solving, we get x = 20000
So, answer is 10000 & 20000
Answer = C
Answer: (C) x = $10,000, y = $20,000.
Question: In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
(A) 289
(B) 190
(C) 277
(D) 266
(E) 255
Rationale: Time taken by B run 1000 meters = (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer:B
Answer: (B) 190
Question: Q=(429)^2 * 237 * (1243)^3 is thrice of ?
(A) 33605 * 31960 * (1243)^2
(B) 33654 * 538219 * (1243)^2
(C) 33891 * 533247 * (1243)^2
(D) 34122 * 532004 * (1243)^2
(E) 34606 * 534572 * (1243)^2
Rationale: Q=(429)^2*237*(1243)^3 is an odd number.
Among answer choices only C is an odd number, (so thrice C also will be an odd number).
Answer: C.
Answer: (C) 33891 * 533247 * (1243)^2
Question: The ratio of the number of ladies to gents at a party was 1:2 but when 2 ladies and 2 gents left, the ratio became 1:3. How many people were at the party originally?
(A) 22
(B) 88
(C) 12
(D) 99
(E) 14
Rationale: x, 2x
(x-2):(2x-2) = 1:3
3x-6 = 2x-2
x = 4
x+2x = 3x
=> 3*4 = 12
Answer: C
Answer: (C) 12
Question: Hydraulic press Machines P and Q are two different machines that cover jars in a factory. When Machine P works alone, it covers 5 jars in m hours. When Machines P and Q work simultaneously at their respective rates, they cover 5 jars in n hours. In terms of m and n, how many hours does it take Machine Q, working alone at its constant rate, to cover 5 jars?
(A) m
(B) n
(C) m+n
(D) 5n/25-mn
(E) m-n
Rationale: working rate p = 5/m ; working rate pq =( 1/p +1/q)* n =5 or mn/5 +n/q =5 0r n/q = 5-mn/5 = 25-mn/5
q = 5n/25-mn
E
Answer: (E) m-n
Question: If 6^w is a factor of (10!)^2, What is the greatest possible value of w ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: w 10!= 10*9*8*7*6*5*4*3*2*1 = 2*5*3*3*2*2*2*7*2*3*5*2*2*3*2 = 2^8*3^4*5^2*7
6= 2*3
Therefore only the exponents of 2 and 3 are relevant, 2^8 or 3^4 -> higher number counts = 8 -> Answer Choice D
Answer: (D) 8
Question: A library has an average of 500 visitors on Sundays and 140 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :
(A) 100
(B) 200
(C) 300
(D) 400
(E) 550
Rationale: Explanation:
Since the month begins with a Sunday, so there will be five Sundays in the month,
Required average = (500 * 5 + 140 * 25) / 30 = 6000/30 = 200
Answer: B) 200
Answer: (B) 200
Question: What is 35% of 4/13 of 650?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 650, or 1/9 of 650. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 650 is a bit more than 630, so (1/9)*630 will be about 70.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The answer is C.
Answer: (C) 70
Question: A starts a business with $3500. After 5 months, B joins with A as his partner. After a year, the profit is divided in the
ratio 2 : 3. B's contribution in the capital is
(A) 7000
(B) 9000
(C) 8000
(D) 9900
(E) 7900
Rationale: Ratio in which profit is divided =2:3
Assume that B's contribution to the capital=b
3500×12:b×7=2:3
⇒3500×12×3=2×b×7
⇒b = 3500×12×3 / 2×7
=500×6×3=9000
ANSWER:B
Answer: (B) 9000
Question: Together, Victor and Tami Vargas earn $33,280 per year. Tami earns $4,160 more per
year than Victor earns. How much do Tami earn per year?
(A) $28,720
(B) $8,720
(C) $18,720
(D) $38,720
(E) $58,720
Rationale: You are asked to find two unknown amounts. Victor’s earnings: x
Represent the amounts using algebra. Tami’s earnings: x 4,160
Write an equation showing that the sum of the
two amounts is $33,280. Solve the equation. x x 4,160 33,280
Combine like terms. 2x 4,160 33,280
Subtract 4,160 from both sides of the equation. 2x 4,160 4,160 33,280 4,160
2x 29,120
Divide both sides by 2.
x 14,560
Now go back to the beginning, when you first wrote the amounts in algebraic language. Since
x represents Victor’s earnings, you know that Victor earns $14,560 per year. Tami’s earnings are
represented by x+4,160. Add: 14,560+4,160=18,720. Tami earns $18,720 per year.
Answer: Victor earns $14,560, and Tami earns $18,720.
correct answer C
Answer: (C) $18,720
Question: A man invested Rs. 14,400 in Rs. 100 shares of a company at 20% premium.If the company declares 7% dividend at the end of the year,then how much does he get ?
(A) Rs. 500
(B) Rs. 840
(C) Rs. 650
(D) Rs. 720
(E) None
Rationale: Solution
Number of shares = (14400/120) = 120.
Face value = Rs. (100x120 ) = Rs. 12000.
Annual income = Rs.(7/100x12000) = Rs. 840.
Answer B
Answer: (B) Rs. 840
Question: A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
(A) 277
(B) 277
(C) 120
(D) 882
(E) 272
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: C
Answer: (C) 120
Question: Four dice are thrown simultaneously. Find the probability that all of them show the same face.
(A) 1/216
(B) 1/215
(C) 5/300
(D) 1/415
(E) 1/500
Rationale: Total no of elementary events = 6^4
n(S) = 6^4
x={(1,1,1,1)(2,2,2,2).....(6,6,6,6)}
n(X)=6
n(X)/n(S) =6/6^4
=1/216
ANSWER A
Answer: (A) 1/216
Question: Working at their respective constant rates, Paul, Abdul and Adam alone can finish a certain work in 3, 4, and 5 hours respectively. If all three work together to finish the work, what fraction R of the work will be done by Adam?
(A)  1/4
(B)  12/47
(C)  1/3
(D)  5/12
(E)  20/47
Rationale: Let the total work be 60 units. Pual does 60/3 =20 units of work per hr. abdul does 15 units per hr and adam does 12 units per hr. If all work together they do (20 + 15 + 12) units per hr = 47 units per hr. So the time taken to finish the work = 60/47 hrs.
adam will do 60/47 * 12 units of work in 60/47 hr . fraction of work adam does =work done by adam / total work
R>( 60/47 *12)/60 =12/47
Answer B
Answer: (B)  12/47
Question: If five numbers are randomly selected without replacement from set {1, 2, 3, 4, 5}, what is the probability that the numbers are selected in ascending order?
(A) 1/256
(B) 1/120
(C) 1/480
(D) 1/240
(E) 1/50
Rationale: The total number of ways to arrange 5 numbers is 5! = 120.
There is only one way to arrange the numbers in ascending order.
P(ascending order) = 1/120
The answer is B.
Answer: (B) 1/120