mathewhe/aqua_rat huggingface dataset:
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m, what is its area?
(A) 2800 m2
(B) 2740 m2
(C) 2520 m2
(D) 2200 m2
(E) 2500 m2
Rationale: Explanation:
length = breadth +23. Therefore,
4×4× breadth +2×23=206 m
⇒ breadth =40 m
length =40+23=63 m
Area =63×40=2520 m2
Answer: Option C
Answer: (C) 2520 m2
Question: For a certain set, the value range of its members is 104.8. A new set is created from the members of the old set as follows: 12 is subtracted from a member of the old set, and the result is divided by 4. The resulting value is a member of the new set. If this operation is done for each member of the old set, what is the range of values of the members of the new set?
(A) 23.2
(B) 26.2
(C) 52.4
(D) 98.4
(E) 104.8
Rationale: Let x and z be the smallest and largest of the original set, respectively.
z - x = 104.8
The smallest and largest members of the new set will be (x-12) / 4 and (z-12) / 4.
Then the range is (z-12) / 4 - (x-12) / 4 = (z-x) / 4 = 104.8 / 4 = 26.2
The answer is B.
Answer: (B) 26.2
Question: If x = 3 and y = -2, what is the value of 2(x-y)^2 - xy ?
(A) 152
(B) 142
(C) 121
(D) 56
(E) 111
Rationale: x = 3 and y = -2
x-y = 3 - (-2) = 3+2 =5
x*y = 3 * -2 = -6
Now we apply it in the equation 2(x-y)^2 - xy =2 (5)^2-(-6)
==>2*25 +6 = 50+6 =56
Answer : D
Answer: (D) 56
Question: How many liters of a 40% iodine solution need to be mixed with 35 liters of a 20% iodine solution to create a 30% iodine solution?
(A) 30.5
(B) 49
(C) 100
(D) 105
(E) 140
Rationale: Solution 1:
Assume the iodine solution to be mixed = x lts.
Iodine = 0.4x lts, Water = 0.6x lts.
Solution 2: 35 liters of a 20% iodine solution
Iodine = 7 lts, Water = 28 lts.
Total iodine = 0.4x + 7
Total water = 0.6x + 28
The resultant is a 35% idoine solution.
Hence (0.4x + 7) / (x + 35) = 30/100
40x + 700 = 30x + 1050
10x = 305
x = 30.5 lts
Correct Option: A
Answer: (A) 30.5
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 992
(C) 772
(D) 662
(E) 552
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: A
Answer: (A) 200
Question: The ratio between the number of sheep and the number of horses at the Stewar farm is 5 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??
(A) 18
(B) 28
(C) 40
(D) 56
(E) 58
Rationale: et no of sheep and horses are 5k and 7k
no of horses= 12880/230=56
now 7K=56 and k=8
no of sheep=(5*8) =40
ANSWER:C
Answer: (C) 40
Question: Tomy's age 22 years hence will be thrice his age four years ago. Find Tomy's present age?
(A) 12 years
(B) 13 years
(C) 15 years
(D) 17 years
(E) 18 years
Rationale: Let MTomy's present age be 'x' years.
x+ 22 = 3(x- 4)
=> 2x = 34 => x = 15 years.
D
Answer: (D) 17 years
Question: The maximum number of student amoung them 1802 pens and 1203 pencils can be distributed in such a way that each student gets the same number of pens and same number of pencils is :
(A) 1
(B) 10
(C) 11
(D) 19
(E) None of these
Rationale: Solution
Required number of student = H.C.F of 1802 and 1203 = 1. Answer A
Answer: (A) 1
Question: If w = 9/25, c = 15/32, and m + w + c = 1, which of the following gives the values of m, w, and c in increasing order?
(A) c, m, w
(B) c, w, m
(C) m, w, c
(D) w, c, m
(E) w, m, c
Rationale: Answer C - m, w, c
w ~ 1/3
c ~ 1/2
and m+w+c = 1 hence m ~ 1/6
Hence increasing order would be m -> w -> c
Answer C
Answer: (C) m, w, c
Question: Which of the following expressions are different in value?
(A) (2x + 3y)2
(B) (2x + y)2 + 8y(x + y)
(C) (2x – y)2 – 8y(x + y)
(D) 22(x + y)2 + 4xy + 5y2
(A) A and B
(B) B and C only
(C) A, B and D only
(D) B and D only
(E) All are different
Rationale: All others are equal except (C).
Answer B
Answer: (B) B and C only
Question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train?
(A) 488
(B) 200
(C) 289
(D) 150 metre
(E) 822
Rationale: Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m.Answer:D
Answer: (D) 150 metre
Question: Machine A can finish a job in 4 hours, Machine В can finish the job in 12 hours, and Machine С can finish the job in 8 hours. How many hours will it take for A, B, and С together to finish the job?
(A) 15/4
(B) 18/7
(C) 21/8
(D) 24/11
(E) 28/13
Rationale: The combined rate is 1/4+1/12+1/8 = 11/24 of the job per hour.
The time to complete the job is 24/11 hours.
The answer is D.
Answer: (D) 24/11
Question: In Kaya's teacher's desk there are 4 pink highlighters, 2 yellow highlighters, and 5 blue highlighters. How many highlighters are there in all?
(A) 11
(B) 22
(C) 77
(D) 33
(E) 88
Rationale: Add the numbers of highlighters.
4 + 2 + 5 =11.
Answer is A.
Answer: (A) 11
Question: For any integer p, *p is equal to the product of all the integers between 1 and p, inclusive. How many prime numbers are there between *4 + 3 and *4 + 4, inclusive?
(A)  None
(B)  One
(C)  Two
(D)  Three
(E)  Four
Rationale: Generally *p or p! will be divisible by ALL numbers from 1 to p. Therefore, *4 would be divisible by all numbers from 1 to 4.
=> *4+3 would give me a number which is a multiple of 3 and therefore divisible (since *4 is divisible by 3)
In fact adding anyprimenumber between 1 to 4 to *4 will definitely be divisible.
So the answer is none (A)!
Supposing if the question had asked for prime numbers between *4 + 3 and *4 + 11 then the answer would be 1. For *4 +3 and *4 + 13, it is 2 and so on...
A
Answer: (A)  None
Question: On a partly cloudy day, milton decides to walk back from work. When it is sunny, he walks at a speed of s miles/hr (s is an integer) and when it gets cloudy, he increases his speed to (s + 1) miles/hr. If his average speed for the entire distance is 2.8 miles/hr, what fraction of the total distance did he cover while the sun was shining on him?
(A) 1/5
(B) 1/6
(C) 1/4
(D) 1/7
(E) 1/3
Rationale: If s is an integer and we know that the average speed is 2.8, s must be = 2. That meanss+1= 3. This implies that the ratio of time for s=2 is 1/4 of the total time. The formula for distance/rate is D=Rt...so the distance travelled when s=2 is 2t. The distance travelled for s+1=3 is 3*4t or 12t. Therefore, total distance covered while the sun was shining over him is 2/14 = 1/7. Answer: D
Answer: (D) 1/7
Question: If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 4 miles?
(A) 12/5
(B) 12/3
(C) 12/4
(D) 12/6
(E) 12/2
Rationale: 1 km is approxmately equal to 0.6 miles
So 4 km = 4*0.6 = 2.4 miles . Multiple & divide by 10
i.e 2.4*10/10 = 24/10 = 12/5
Answer : A
Answer: (A) 12/5
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 seconds. The speed of the train is?
(A) 66
(B) 77
(C) 88
(D) 50
(E) 33
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 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: D
Answer: (D) 50
Question: The average monthly salary of 24 employees in an organisation is Rs. 2400. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary?
(A) Rs.3601
(B) Rs.3618
(C) Rs.4900
(D) Rs.3619
(E) Rs.3610
Rationale: Manager's monthly salary
= Rs. (2500 * 25 - 2400 * 24)
= Rs.4900 Answer:C
Answer: (C) Rs.4900
Question: Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 4 litres from vessel P is mixed with 8 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is?
(A) 19:1
(B) 19:4
(C) 19:8
(D) 38:10
(E) 38:2
Rationale: Quantity of alcohol in vessel P = 62.5/100 * 4 = 5/2 litres
Quantity of alcohol in vessel Q = 87.5/100 * 8 = 7/1 litres
Quantity of alcohol in the mixture formed = 5/2 + 7/1 = 19/2 = 9.50 litres
As 12 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 9.50 : 2.50 = 38:10.
Answer: D
Answer: (D) 38:10
Question: Each child has 2 pencils and 13 Skittles. If there are 8 children, how many pencils are there in total?
(A) 16
(B) 12
(C) 18
(D) 22
(E) 08
Rationale: 2*8=16.Answer is A.
Answer: (A) 16
Question: The product Z of two prime numbers is between 10 and 30 . If one of the prime numbers is greater than 2 but less than 6 and the other prime number is greater than 6 but less than 24, then what is Z?
(A) 21
(B) 15
(C) 14
(D) 10
(E) 6
Rationale: The smallest possible product is 21 which is 3*7.
All other products are too big.
The answer is A.
Answer: (A) 21
Question: In the class of 50 students, 30 speak Tamil and 40 speak Telugu. What is the lowest possible number of students who
speak both the languages?
(A) A)8
(B) B)10
(C) C)20
(D) D)30
(E) E)32
Rationale: let the student who speaks Tamil-x
let the student who speaks Telugu-y
as (xuy)-(xny)=total
30+40-(xny)=50
=20
C)
Answer: (C) C)20
Question: Mother is aged 3times more than her daughter Rose. After 8 years, she would be two and a 1/2times of Rose's age. After further 8 years, how many times would he be of Rose's age?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let Ronit's present age be x years. Then, father's present age =(x + 3x) years = 4x years.
(4x + 8) = 5 (x + 8)
2
8x + 16 = 5x + 40
3x = 24
x = 8.
Hence, required ratio = (4x + 16)/(x + 16) = 48/24= 2.
B
Answer: (B) 2
Question: In a 300 member association consisting of men and women, exactly 80% of men and exactly 15% women are homeowners. What is the least number of members who are homeowners?
(A) 46
(B) 47
(C) 48
(D) 49
(E) 50
Rationale: Solution simple
Out of 300 80% are male i.e 240 and 15% are female i.e 45 , so total homeowner is 295.
Now min number homeowner is 45 and max is 240 so question ask us to find least and 46 has least value among all option.
So ans is 46.
Ans: A
Answer: (A) 46
Question: The sum of three consecutive odd natural numbers, each divisible by 3 is 78. What is the largest among them?
(A) 21
(B) 24
(C) 29
(D) 36
(E) 45
Rationale: Let the 3 consecutive odd numbers each divisible by 3 be X, X+3, X+6
Given, X + X+3 + X+6 = 78
3X = 69
X = 23
The numbers are 23, 26, 29
Therefore the largest number is 29
Answer C.
Answer: (C) 29
Question: The average monthly income of P and Q is Rs. 2050. The average monthly income of Q and R is Rs. 5250 and the average monthly income of P and R is Rs. 6200. The monthly income of R is:
(A) 5100
(B) 4900
(C) 9400
(D) 1500
(E) 3200
Rationale: Explanation:
Let P, Q and R represent their respective monthly incomes. Then, we have:
P + Q = (2050 x 2) = 4100 .... (i)
Q + R = (5250 x 2) = 10500 .... (ii)
P + R = (6200 x 2) = 12400 .... (iii)
Adding (i), (ii) and (iii), we get: 2(P + Q + R) = 27000 or P + Q + R = 13500 .... (iv)
Subtracting (i) from (iv), we get P = 9400.
P's monthly income = Rs. 9400.
Answer: C
Answer: (C) 9400
Question: A person crosses a 720 m long street in 12 minutes. What is his speed in km per hour?
(A) 3.6
(B) 4.5
(C) 4.8
(D) 5.4
(E) 5.5
Rationale: Speed = 720/(12x60) m/sec
= 1 m/sec.
Converting m/sec to km/hr =1 x(18/5) km/hr
= 3.6 km/hr.
ANSWER :A
Answer: (A) 3.6
Question: A person want to give his money of $900 to his 3 children A,B,C in the ratio 2:3:4. What is the B's share?
(A) $400
(B) $300
(C) $500
(D) $180
(E) $200
Rationale: B's share = 900*3/9 = $300
Answer is B
Answer: (B) $300
Question: FAG, GAF, HAI, IAH, ____
(A) SIK
(B) IKP
(C) PLE
(D) JAK
(E) EWR
Rationale: The middle letters are static, so concentrate on the first and third letters. The series involves an alphabetical order with a reversal of the letters. The first letters are in alphabetical order: F, G, H, I , J. The second and fourth segments are reversals of the first and third segments. The missing segment begins with a new letter.
ANSWER:D
Answer: (D) JAK
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 225 m
(C) 245 m
(D) 250 m
(E) 260 m
Rationale: Explanation:
Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
ANSWER IS C
Answer: (C) 245 m
Question: It takes Jim two hours to wash the car and it takes Julia one hour to wash the car. Working together, how many minutes will it take them to wash the car?
(A) 36
(B) 38
(C) 40
(D) 42
(E) 44
Rationale: Jim can wash (1/2) of the car per hour.
Julia can wash 1 car per hour.
Together they can wash 1/2+1=3/2 cars per hour.
1 car / (3/2) cars per hour = 2/3 hours = 40 minutes.
The answer is C.
Answer: (C) 40
Question: If the cost price is 96% of selling price then what is the profit percentage.
(A) 7.14
(B) 7.41
(C) 4.71
(D) 4.17
(E) None of them
Rationale: selling price=Rs100 : then cost price=Rs 96:profit =Rs 4.
Profit={(4/96)*100}%=4.17%
Answer is D.
Answer: (D) 4.17
Question: After spending Rs. 5000 on rent, Rs. 1500 on milk, Rs. 4500 on groceries, Rs.2500 On childrens education Rs. 2000 on petrol and Rs. 2500 on miscellaneous expenses, Mr. Kishore saved 10% of his monthly salary. How much did he save in Rs. ?
(A) 2160
(B) 2350
(C) 2000
(D) 2300
(E) None of these
Rationale: Explanation :
Total Exp = 5000+1500+4500+2500+2000+2500 = 18000
Exp in % = 100-10 = 90%, 18000 = 90%
Saving = 10 % = 18000 X 10/90 = Rs. 2000
Answer : C
Answer: (C) 2000
Question: The least number which should be added to 6320 so that the sum is exactly divisible by 4, 6, 7 and 9 is:
(A) 112
(B) 212
(C) 252
(D) 239
(E) 232
Rationale: L.C.M. of 5, 6, 4 and 3 = 252.
On dividing 6320 by 252, the remainder is 20.
Number to be added = (252 - 20) = 232. Answer: Option 'E'
Answer: (E) 232
Question: The price of commodity X increases by 45 cents every year, while the price of commodity Y increases by 20 cents every year. In 2001, the price of commodity X was $4.20 and the price of commodity Y was $6.30. In which year will the price of commodity X be 65 cents more than the price of commodity Y?
(A) 2010
(B) 2011
(C) 2012
(D) 2013
(E) 2014
Rationale: The price of commodity X increases 25 cents each year relative to commodity Y.
The price difference is $2.10 and commodity X needs to be 65 cents more than commodity Y.
$2.75 / 25 cents = 11 years
The answer is 2001 + 11 years = 2012.
The answer is C.
Answer: (C) 2012
Question: How long does a train 120 m long running at the speed of 70 km/hr takes to cross a bridge 150 m length?
(A) 12.7 sec
(B) 13.9 sec
(C) 18.1 sec
(D) 17.1 sec
(E) 19.7 sec
Rationale: Speed = 70 * 5/18
= 19.4 m/sec
Total distance covered
= 120 + 150 = 270 m.
Required time = 270/19.4 '
= 13.9 sec.
Answer:B
Answer: (B) 13.9 sec
Question: When running a mile during a recent track meet, Nuria was initially credited with a final time of 5 minutes, 39 seconds. Shortly after her run, officials realized that the timing mechanism malfunctioned. The stopwatch did not begin timing her until 11/25 of a minute after she began to run. If the time was otherwise correct, how long did it actually take Nuria to run the mile?
(A) 5 minutes, 17.6 seconds
(B) 6 minutes, 10.4 seconds
(C) 5 minutes, 43.56 seconds
(D) 5 minutes, 44.44 seconds
(E) 5 minutes, 21.8 seconds
Rationale: One approach:
The watch starts to work after Nuria began his running. It means the time should be greater than credited 5 minutes, 44 seconds. The only number is 6 minutes, 10.4 seconds.
Another approach:
11/25 close to 30 second when added to the 5 minutes, 44 seconds, it means it passes 6 minute.
Answer: B
Answer: (B) 6 minutes, 10.4 seconds
Question: Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements W are possible?
(A)  30
(B)  60
(C)  90
(D)  180
(E)  540
Rationale: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.
But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.
I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements W including the order of tasks.
could you explain the highlighted step... i'm getting 90 = 15 * 3!
suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z
one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways
X--	Y--	Z
12--	34--	56
12--	56--	34
34--	12--	56
34--	56--	12
56--	12--	34
56--	34--	12
so the answer should be 15*6 = 90
But now you can fruther decide which task you want to perform first X Y or Z..=C
Answer: (C)  90
Question: 1+2+2^2=？
(A) (2^3-1)(2^3+1)
(B) 2^6+1
(C) 2^5-1
(D) 2^5+1
(E) 2^3-1
Rationale: From 1+2+2^2=1(2^6-1)/(2-1)=2^3-1, the correct answer is E.
Answer: (E) 2^3-1
Question: There are three piles of books A,B and C having 3,4,5 books respectively.These books have to be picked up and put in a shelf one by one.How many possible sequence can be formed in the shelf if a book can be picked only from top of any pile?
(A) 12!
(B) 3!*4!*5!
(C) 12C3*9C4
(D) 12^12
(E) 12^14
Rationale: SINCE WE SHOULD FILL ONLY FROM TOP.........12! IS NOT CORRECT
WE HAVE POSSIBILTY OF FILLING ALL 5 FROM C AND GO TO A,B 0R 1 EACH FROM EACH PILE OR 2..........SO 3!*4!*5! AND 12C3*9C4 ARE ALSO WRONG.REMAINING OPTION IS ........12^12
ANSWER:D
Answer: (D) 12^12
Question: If a train, travelling at a speed of 120 kmph, crosses a pole in 6 sec, then the length of train is?
(A) 281
(B) 125
(C) 200
(D) 266
(E) 121
Rationale: D = 120* 5/18 * 6
= 200 m
Answer: C
Answer: (C) 200
Question: 3 women and a few men participated in a chess tournament. Each player played two matches with each of the other players. If the number of matches that men played among themselves is 78 more than those they played with the women, how many more men than women participated in the tournament?
(A) 10
(B) 11
(C) 8
(D) 9
(E) 5
Rationale: Let x be the number of men.
Number of matches men play among themselves is 2*(xC2)
Number of matches men play with women is 2*(3x)
2*(xC2) - 2*(3x) =78
x=13
Difference between men and women is 13-3=10.
ANSWER A
Answer: (A) 10
Question: What is the remainder when 43^87 is divided by 5?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The units digit of the exponents of 3 cycle in a group of 4: {3, 9, 7, 1}
87 has the form 4k+3 so the units digit of 43^87 is 7.
The remainder when dividing by 5 is 2.
The answer is C.
Answer: (C) 2
Question: A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution?
(A) 72.8 litres
(B) 72.9 litres
(C) 74.9 litres
(D) 72.4 litres
(E) 72.7 litres
Rationale: Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally in the vessel
= [(90 - 9)/90]2 (90) = 72.9 litres.
Answer:B
Answer: (B) 72.9 litres
Question: Convert the 13/36 m/s into kilometers per hour?
(A) 1.7
(B) 1.5
(C) 1.3
(D) 1.1
(E) 1.2
Rationale: 13/36 m/s = 13/36 * 18/5 = 13/10
= 1.3 kmph.
Answer: C
Answer: (C) 1.3
Question: Two letters from the word MYANTKAR are selected at random. What is the probability that at least one of the selected letters is a consonant?
(A) 27/28
(B) 25/28
(C) 29/28
(D) 32/28
(E) 42/28
Rationale: There are 6 consonants and 2 vowels in MYANTKAR .
probability that at least one of the selected letters is a consonant = 1 - (Probability of both vowels)
Probability of both vowels = 2C2/8C2 = 1/28
So,Answer is 1 - 1/28 = 27/28
Answer : A
Answer: (A) 27/28
Question: If 6 (A's capital) = 8 (B's capital) = 10 (C's capital). Then the ratio of their capitals is?
(A) 20:15:17
(B) 20:15:19
(C) 20:15:12
(D) 20:15:18
(E) 20:15:23
Rationale: 6A = 8B = 10 C
A:B:C = 1/6:1/8:1/10
= 20:15:12
Answer: C
Answer: (C) 20:15:12
Question: At the rate of 6%p.a SI, a sum of Rs. 2500 will earn how much interest by the end of 5 years?
(A) 750
(B) 650
(C) 250
(D) 980
(E) 950
Rationale: 2500--->5 * 6%= 30%(2500) =750Ans A
Answer: (A) 750
Question: If n is a prime number greater than 5, what is the remainder when n^2 is divided by 23?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question including the one under the spoiler. But the easiest way is as follows:since we can not have two correct answersjust pick a prime greater than 5, square it and see what would be the remainder upon division of it by 23.
n=5 --> n^2=49 --> remainder upon division 49 by 23 is 3.
Answer: D.
Answer: (D) 3
Question: If the compound interest on a certain sum for 2 years in Rs. 80.80 and the simple interest Rs. 80; then the rate of interest per annum is
(A) 2%
(B) 1%
(C) 3%
(D) 4%
(E) 5%
Rationale: Explanation:
Let the sum be P and Rate of Interest be R% per annum
Simple Interest on Rs.P for 2 years = 80
PRT/100 = 80
(PR × 2)/100 = 80
PR/50 = 80
PR = 4000 - -- (equation 1)
Compound Interest = P(1 + R/100)T - P
= P(1 + R/100)2 - P
= P[(1 + R/100)2 - 1] = P[(1 + 2R/100 + R2/10000) - 1] = P(2R/100 + R2/10000)
= 2PR/100 + PR2/10000
= 2PR/100 + (PR × R)/10000
= [2 × 4000]/100 + (4000 × R)/10000 ( substituted the value of PR from equation 1)
= 80 + 0.4R
Given that compound interest = Rs.80.80
=> 80 + 0.4R = 80.80
=> 0.4R = 0.80
=> R = 0.80/0.4 = 2%
Answer: Option A
Answer: (A) 2%
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
(A) 63
(B) 93
(C) 103
(D) 83
(E) 135
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) =	(7 x 6/2 x 1) x 3= 63.
Answer : A.
Answer: (A) 63
Question: A train moves past a post and a platform 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?
(A) 79.0
(B) 79.2
(C) 79.5
(D) 79.7
(E) 79.6
Rationale: Let x is the length of the train and v is the speed
Time taken to move the post = 8 s
=> x/v = 8
=> x = 8v --- (1)
Time taken to cross the platform 264 m long = 20 s
(x+264)/v = 20
=> x + 264 = 20v ---(2)
Substituting equation 1 in equation 2, we get
8v +264 = 20v
=> v = 264/12 = 22 m/s
= 22×36/10 km/hr = 79.2 km/hr
Answer is B.
Answer: (B) 79.2
Question: Find the remainder when 10,000 is divided by 84
(A) 4
(B) 1
(C) 6
(D) 7
(E) 8
Rationale: Answer:A
Answer: (A) 4
Question: The difference of 2 digit number & the number obtained by interchanging the digits is 36. What is the difference the sum and the number if the ratio between the digits of the number is 1:2 ?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Let the number be xy.
Given xy – yx = 36.
This means the number is greater is than the number got on reversing the digits.
This shows that the ten’s digit x > unit digit y.
Also given ratio between digits is 1 : 2 => x = 2y
(10x + y) – (10y +x) = 36 => x – y = 4 => 2y – y =4.
Hence, (x + y) – (x – y) = 3y – y = 2y = 8
B
Answer: (B) 8
Question: xy=1 then what is (4^(x+y)^2) / (4^(x-y)^2)
(A) 256
(B) 4
(C) 8
(D) 16
(E) 32
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
4^4 = 256
Answer A
Answer: (A) 256
Question: A certain galaxy is known to comprise approximately 4 x 10^12 stars. Of every 50 million of these stars, one is larger in mass than our sun. Approximately how many stars in this galaxy are larger than the sun?
(A) 800
(B) 1,250
(C) 8,000
(D) 12,000
(E) 80,000
Rationale: 4*10^12
50 mln = 5*10^7
we divide 10^12 by 10^7 and we get (10^5)*4 = 400,000 and divide by 5. the result is 80,000
E
Answer: (E) 80,000
Question: If a book is sold at 5% profit instead of 5% loss, it would have brought Rs 13 more. Find out the cost price of the book
(A) 75
(B) 72
(C) 130
(D) 70
(E) 80
Rationale: Let C.P. of the book be Rs. ’X’
Given, 1.05 X - 0.95X = 13
=> 0.1 X = 13 = 13/0.1 = Rs 130
ANSWER:C
Answer: (C) 130