MU-NLPC/Calc-aqua_rat huggingface dataset:
If f and g are distinct prime numbers less than 10, which of the following cannot be the product of f and g?	Pick one:
A) 6  B) 9  C) 10  D) 14  E) 15

Solution: prime numbers less than 10 are 2, 3, 5, 7   all except 9 is product of any two numbers picked from above set.   Ans: 9
Answer: B
Each cell of a certain kind of bacteria produces two more cells. The life span of each cell is 10 minutes and each cell multiples only once in its life time, when it is exactly one minute old. If a new cell is placed in an empty box at time t = 0, then how many live cells will be there in the box just after t = 20 minutes?  Choose the correct choice from the following choices
A) 2048 × 1023	B) 1024 × 1023	C) (1024)²	D) 1023 × 1025	E) 1023 × 1026

Solution: see total cells created after   1min be 2^1   2min be 2^2   3 min be 2^3.......   thus after 20 min 2^20 will be created   now after 10 min 1 cell will die (2^0)   after 11 min 2 cells die (2^1)   similarly after 20 min 2^10 cells die   thus total cells remained=(2^20)-(1024)   or (1024)^2-1024   or1024*(1024-1)   i.e, 1024*1023   ANSWER:1024 × 1023
Answer: B
Two twins sisters Sita and Geeta were standing back to back and suddenly they started running in opposite directions for 6 km each. Then they turned left and ran for another 4.5 km.
What is the distance (in kilometers) between the the two twins when they stop?
Choose the correct choice from the following choices
A) 12 B) 15 C) 18 D) 21 E) 24

Solution: The distance between them is the hypotenuse of a right angle triangle with sides 9 km and 12 km.   hypotenuse = sqrt(9^2 + 12^2) = 15   The answer is 15.
Answer: B
In a certain alphabet, 13 letters contain a dot and a straight line. 24 letters contain a straight line but do not contain a dot. If that alphabet has 40 letters, all of which contain either a dot or a straight line or both, how many letters contain a dot but do not contain a straight line?
Choose the correct choice from the following choices
A) 3 B) 8 C) 14 D) 20 E) 28

Solution: We are told that all of the letters contain either a dot or a straight line or both, which implies that there are no letters without a dot and a line (no line/no dot box = 0).   First we find the total # of letters with lines:  13 +24= 
 13 +24 = 37
37;   Next, we find the total # of letters without line:  40 - 37= 
 40 - 37 = 3
3;   Finally, we find the # of letters that contain a dot but do not contain a straight line:  3 - 0= 
  3 - 0 = 3
3.   3
Answer: A
24 is divided into two parts such that 7 times the first part added to 5 times the second part gives 146. The first part is	Choose the correct choice from the following answers
A) 11 B) 13 C) 16 D) 17 E) None

Solution: Explanation:   Let the first and second parts be a and 24 a, then   7a+5(24−a)=146   ⇒7a+120−5a=146   ⇒2a=26 or a = 13   Correct Option: 13
Answer: B
If a code word is defined to be a sequence of different letters chosen from the 10 letters A, B, C, D, E, F, G, H, I, and J, what is the ratio of the number of 6-letter code words to the number of 4-letter code words?
Options:
A) 5 to 4
B) 30 to 1
C) 2 to 1
D) 5 to 1
E) 6 to 1

Solution: Number of ways to form 6-letter code: 10!/4! = 10*9*8*7*6*5   Number of ways to form 4-letter code: 10!/6! = 10*9*8*7   Ratio: 30 to 1   Answer : 30 to 1
Answer: B
An amount of Rs. 3000 becomes Rs. 3600 in four years at simple interest. If the rate of interest was 1% more, then what was be the total amount?	Select the correct option
A) 3729
B) 2799
C) 3720
D) 2884
E) 2881

Solution: A = P(1 + TR/100)   => 3600 = 3000[1 + (4 * R)/100] => R = 5%   Now R = 6%   => A = 3000[1 + (4 * 6)/100] = Rs. 3720.   Answer:3720
Answer: C
Jaime earned enough money by selling seashells at 22 cents each to buy several used paperback books at 55 cents each. If he spent all of the money he earned selling seashells to buy the books, what is the least number of seashells he could have sold ?  Choose the correct answer:
A) 5 B) 11 C) 17 D) 25 E) 30

Solution: Let's TEST Answer A: 5 seashells...   With 5 seashells, Jamie would have 5(22) = 110 cents. This would allow him to buy 2 books for 110 cents total, so this is the correct answer.   5
Answer: A
Which number is the odd one out ?
9654 4832 5945 7642 7963 8216 3646	Choices:
A) 3646
B) 9654
C) 5945
D) 7963
E) 8216

Solution: The product of first two digits in a number equals the last two digits, except in 3646. Hence, it is the odd one.   The answer is 3646.   3646NSWER:3646
Answer: A
Mr. Karan borrowed a certain amount at 6% per annum simple interest for 9 years. After 9 years, he returned Rs. 8410/-. Find out the amount that he borrowed. Answers:  A) s. 5266  B) s. 5269  C) s. 5461  D) s. 5218  E) s. 52192

Solution: Explanation:   Let us assume Mr. Karan borrowed amount is Rs. A. (the principal)   By formula of simple interest, S.I. = PRT / 100   Where P = The principal, R = Rate of interest as a %, T = Time in years   S.I. = (P * 6 * 9)/100 = 54 P/100   Amount = Principal + S.I.   8410 = P + (54P/100)   8410 = (100P + 54P)/100   8410 = 154P/100   P = (8410 * 100)/154 = Rs. 5461.039   ANSWER: s. 5461
Answer: C
If 15648 books need to be placed in boxes and each box can contain at most 9 books. How many books will be in the last unfilled box?
Options:
8 Options:
A) 12 books B) 6 books C) 24 books D) 18 books E) 5 books

Solution: The number of books that can be placed in boxes of 9 books is the first number that is divisible by 9 that occurs before 15648.   In order to divide the sum in 9 parts, the amount must be divisible by 9   Divisibility rule of 9: The sum of the digits must be divisible by 9   Sum of digits of 15648 =24 and 18 is divisible by 9.   Hence, we need to remove 6 to this number for it to be divisible by 9   Correct Option:6 books
Answer: B
The simple interest at x% for x years will be Rs. x on a sum of:
Choose one.
A) x	B) x^2	C) 100x	D) 100x^2	E) 50x^2

Solution: Explanation :   P = ?   R = x%   Simple Interest,SI = x   T = x years   P=100× SI/RT=100 × x / x × x=100/x   Answer : Option 100x
Answer: C
For an integer n greater than 1, n* denotes the product of all the integers from 1 to n inclusive. How many prime numbers are there between 7*+2 and 7*+7, inclusive ?  Choose the correct option:  A) 0  B) 1  C) 2  D) 3  E) 4

Solution: Given that n* denotes the product of all the integers from 1 to n, inclusive so, 7* + 2 = 7! + 2 and 7* + 7 = 7! + 7.   Now, notice that we can factor out 2 our of 7! + 2 so it cannot be a prime number, we can factor out 3 our of 7! + 3 so it cannot be a prime number, we can factor out 4 our of 7! + 4 so it cannot be a prime number, ... The same way for all numbers between 7! + 2 and 7! +7, inclusive. Which means that there are no primes in this range.   0nswer: 0.
Answer: A
What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 54?	Choose the correct choice.
A) 3672
B) 920
C) 7290
D) 6928
E) 3729

Solution: Explanation:   Let the side of the square plot be a ft.   a2 = 289 => a = 17   Length of the fence = Perimeter of the plot = 4a = 68 ft.   Cost of building the fence = 68 * 54 = Rs. 3672.   3672nswer: Option 3672
Answer: A
If the time is currently 1:30 pm, what time will it be in exactly 646 hours?	Pick:
A) 11:30 am
B) 12:30 pm
C) 1:30 pm
D) 2:30 pm
E) 3:30 pm

Solution: 646 = 26(24) + 22/24   The time will be 22 hours later than 1:30 pm which is 11:30 am.   The answer is 11:30 am.
Answer: A
A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 650 m long?	Choose the correct choice from the following choices:
A) 90 sec
B) 89 sec
C) 54 sec
D) 27 sec
E) 22 sec

Solution: Speed = 250/25= 
250/25 = 10
10 m/sec.   Required time= (250 + 650)/10= 
(250 + 650)/10 = 90
90 sec.   90 secnswer: 90 sec
Answer: A
A barrel full of beer has 2 taps one midway,,which draw a litre in 6 minutes and the other at the bottom,which draws a litre in 4 minutes. The lower tap is lower normally used after the level of beer in the barrel is lower than midway.The capacity of the barrel is 36 litres. A new assistant opens the lower tap when the barrel is full and draws out some beer. As a result the lower tap has been used 24 minutes before the usual time. For how long was the beer drawn out by the new assistant ?  Choose the correct choice from the following choices:
A) 15 minutes	B) 16 minutes	C) 17 minutes	D) 18 minutes	E) None of these

Solution: Sol. The top tab is operational till 18 litres is drawn out.   ∴ Time after which the lower tap is usually open   = 18 × 6 = 108 minutes   ∴ Time after which it is open now = 108 – 24 = 84 minutes   ∴ Litres drawn = 84/6= 
84/6 = 14
14 litres   ∴ 18 – 14= 4 litres were drawn by the new assistant.   ∴ Time = 4 × 4 = 16 minutes Answer 16 minutes
Answer: B
One side of a rectangle is 3 cm shorter than the other side. If we increase the length of each side by 1 cm, then the area of the rectangle will increase by 16 cm2. Find the lengths of all sides.  Pick one
A) 10 and 3  B) 9 and 6  C) 10 and 7  D) 3 and 10  E) 10 and 10

Solution: Let x be the length of the longer side x>3, then the other side's length is x−3 cm. Then the area is S1 = x(x - 3) cm2. After we increase the lengths of the sides they will become (x+1) and (x−3+1)=(x−2) cm long. Hence the area of the new rectangle will be A2=(x+1)⋅(x−2) cm2, which is 16 cm2 more than the first area. Therefore   A1+16=A2   x(x−3)+16=(x+1)(x−2)   x2−3x+16=x2+x−2x−2   2x=18   x=9. So, the sides of the rectangle are 9 cm and (9−3)=6 cm long.   So answer is 9 and 6.
Answer: B
Jim drove 768 miles of a 1200 miles journey. How many more miles does he need to drive to finish his journey?  Choose the correct option
A) 432 miles	B) 532 miles	C) 632 miles	D) 732 miles	E) 832 miles

Solution: The number of miles to drive to finish his journey is given by   1200 - 768= 
1200 - 768 = 432
432 miles   correct answer 432 miles
Answer: A
The value of 2*x+x/4+ x(xx) when x = 4 is:
Select the correct option:	A) 57	B) 63	C) 75	D) 73	E) 45

Solution: 2*x+x/4+ x(xx)   2*4+4/4+4(4*4)   2*4+4/4+4(16)   2*4+4/4+64   2*4+1+64   8+1+64= 
8+1+64 = 73
73   answer 73
Answer: D
In the sequence S, each term after the first is twice the previous term. If the first term of sequence S is 3, what is the sum of the 14th, 15th, 16th, 17th and 18th terms in sequence S?
Choose one.
A) 3(2^16)  B) 9(2^15)  C) 21(2^14)  D) 9(2^14)  E) 63(2^13)

Solution: The terms in the sequence can be shown as   a(n) = 2* a(n-1)   So, the sequence will look like: 3, 2*3, (2^2) *3,...   And the nth term will be given as 2^(n-1) *3   Therefore, a(14) = (2^13)*3, a(15) = (2^14) *3, a(16) = (2^15) *3, a(17) = (2^16) *3 and a(18) = (2^17) *3   So, a(14) + a(15) + a(16)+ a(17)+ a(18) = (2^13) *3 + (2^14) *3 + (2^15) *3+ (2^16) *3+ (2^17) *3   = 3* (2^13) *(1+2+4+8+16) = 3* (2^13) *31   = 63 * (2^13)   Answer : 63(2^13)
Answer: E
The length of the bridge, which a train 130 m long and traveling at 45 km/hr can cross in 30 sec is?	Choose the correct choice from the following options: A) 165 m B) 886 m C) 245 m D) 286 m E) 281 m

Solution: Speed = 45 * 5/18   = 25/2 m/sec.   Time = 30 sec   Let the length of bridge be x meters.   Then, (130 + x)/30   = 25/2   x = 245 m.   Answer: 245 m
Answer: C
The radius of a cylindrical vessel is 9cm and height is 3cm. Find the whole surface of the cylinder? Select.
A) 308 sq cm
B) 220 sq cm
C) 440 sq cm
D) 132 sq cm
E) 678.8 sq cm

Solution: r = 9 h = 3   2πr(h + r) = 2 * 22/7 * 9(12) = 678.8   ANSW678.8 sq cmR:678.8 sq cm
Answer: E
The ratio of red boxes to blue boxes in a certain warehouse is 5 to 25. If the number of the red boxes were doubled and the number of blue boxes were increased by 150 the ratio would be halved. How many total boxes are in the warehouse?
Choose the most appropriate option.
A) 60 B) 74 C) 111 D) 148 E) 244

Solution: Ratio = R/B = 5/25 or R = 5/25 B -----------(1)   2R/B+150 = 5/25*1/2 = 1/10 or we can say that 20R=B+150 -------------(2)   solving (1) and (2) we get   B=50 and R =10   so total boxes is B + R = 50+10= 
50+10 = 60
60   Hence A. 60 is the correct answer
Answer: A
There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts R needed to confirm that each of the 5 keys matches each of the 5 locks? Choose the correct option.
A) 5,15
B) 4,15
C) 5,10
D) 4,10
E) 5,20

Solution: Assume you have locks 1-5 and keys A-E.   Minimum: assume you are lucky to find the correct key/combo on the first try. So, 1 -> A, 2 -> B, 3 ->C, and 4 -> D, then 5 must match with E. Therefore, you only need to try 4 combos at a minimum.   Maximum: assume that it takes as many guesses as possible. So, with the first key you try A, B, C, and D with no success, therefore E must be the match (so 4 attempts). For key 2 you no longer have E available so you try A, B, and C, with no success, therefore D must be the match (3 attempts). And so on for key 3 (2 attempts) and key 4 (1 attempt). Key 5 matches with the remaining lock for a total of R=4 + 3 + 2 + 1= 
4 + 3 + 2 + 1 = 10
10 attempts.4,10
Answer: D
A train 100 m in length crosses a telegraph post in 12 seconds. The speed of the train is?
Select the correct option.
A) 16 kmph  B) 30 kmph  C) 54 kmph  D) 18 kmph  E) 19 kmph

Solution: S = 100/12 * 18/5= 
100/12 * 18/5 = 30
30 kmph   Answer: 30 kmph
Answer: B
a,b and c are positive integers less than or equal to 9. If a,b and c are assembled into the six-digit number abcabc, which of the following must be a factor of abcabc? Choices
A) 7
B) 9
C) 11
D) 3
E) none of these

Solution: The sum of the digits in place 1,3 and 5 is a+c+b is equal to the sum of the digits in place 2,4 and 6 which is b+a+c. thus the number abcabc is divisible by 11. thus 11 must be a factor of abcabc.   Answer: 11
Answer: C
If p and q are positive integers each greater than 1, and 17(p+1)=20(q+1), what is the least possible value of p+q?
Choose the correct choice from the following.
A) 35	B) 42	C) 44	D) 46	E) none

Solution: 17(p+1)=29(q+1) --> (p+1)/(q+1) = 20/17 --> the least positive value of p+1 is 20, so the least value of p is 19 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is   19+16= 
  19+16 = 35
35.   35nswer: 35
Answer: A
JOHN and ANDREW can finish John work 30 days if they work together. They worked together for 20 days and then ANDREW left. JOHN finished the remaining work in another 20 days. In how many days JOHN alone can finish the work? Answers:
A) 40
B) 50
C) 55
D) 58
E) 60

Solution: Amount of work done by JOHN and ANDR60W in 1 day = 1/30   Amount of work done by JOHN and ANDR60W in 20 days = 20 × (1/30) = 20/30 = 2/3   Remaining work – 1 – 2/3 = 1/3   JOHN completes 1/3 work in 20 days   Amount of work JOHN can do in 1 day = (1/3)/20 = 1/60   => JOHN can complete the work in 60 days   60
Answer: E
Stacy has a 81 page history paper due in 3 days. How many pages per day would she have to write to finish on time?
Choices:
A) 9	B) 27	C) 10	D) 8.5	E) 6

Solution: 81/3= 
81/3 = 27
27   Answer : 27
Answer: B
The compound interest earned by Sunil on a certain amount at the end of two years at the rate of 8% p.a. was Rs.2828.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.  Choose the correct choice from the following answers
A) 19828.77 B) 19828.8 C) 19828.82 D) 19888.82 E) 19828.22

Solution: Let the sum be Rs.P   P{ [ 1 + 8/100]2 - 1 } = 2828.80   P(8/100)(2 + 8/100) = 2828.80 [a2 - b2 = (a - b) ( a + b)] P = 2828.80 / (0.08)(2.08) = 1360/0.08= 
1360/0.08 = 17_000
17000 Principal + Interest= Rs. 19828.80   Answer: 19828.8
Answer: B
The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? Choose one.
A) 399
B) 272
C) 666
D) 277
E) 311

Solution: Answer: Option 666   Explanation:   a2 = 3136 => a = 56   56 * 4 * 3= 
56 * 4 * 3 = 672
672 â€“ 6= 666 * 1= 
666 * 1 = 666
666 Answer: 666
Answer: C
How many 4-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same?
Choose one:
A) 1236 B) 3528 C) 4096 D) 4608 E) 6561

Solution: First digit.. 9 posibilities   Second digit, 8 possibilities   third digit, 7 possibilities   Fourth digit, 7 possibilities.   9*8*7*7= 
9*8*7*7 = 3_528
3528.   3528
Answer: B
The probability of a team winning a match given Matt is playing the match is 0.70. The probability of the team winning a match given Matt is not playing the match is 0.3. The probability of Matt playing any match is 0.7.
If it is known that the team has won the last match, what is the probability that Matt played the match?
Choose the correct choice from the following answers.
A) A)0.844	B) B)0.7	C) C)0.8571	D) D)0.7531	E) E)0.8213

Solution: Out of 100 matches:   Matt is plays in 70 and not plays in 30.   Out of 70 matches Matt plays in, team wins   0.70*70= 
  0.70*70 = 49
49.   Out of 30 matches Matt does not play in, team wins   0.3*30= 
  0.3*30 = 9
9.   So, out of 100 matches 49 + 9= 
49 + 9 = 58
58 are won.   It is known that the team has won the last match. Out of 58 matches won, Matt is in 49: 49/58= 0.844...   0.844nswer: 0.844.
Answer: A
In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 4 boys when No boy gets more than one prize?	Choose the most appropriate option:
A) 12
B) 51
C) 21
D) 24
E) 25

Solution: Sol. In this case, repetitions are not allowed. So, the first prize can be given in 4 ways. The second in 3 ways and the third in 2 ways. But fundamental principle, (4 x 3 x 2) ways = 24 ways   4: Or 4p = — 4:- 4X3X2X1- 24 ways   24
Answer: D
The product X of two prime numbers is between 15 and 70. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X = Choose one:
A) 18 B) 29 C) 37 D) 44 E) 69

Solution: Option BC can be ruled out as they themselves are prime numbers   18 = 2*9 = 3*6 >> Ignore   44 = 2 * 22 = 4 * 11 >> Ignore   69= 3*23= 
3*23 = 69
69
Answer: E
Murali travelled from city A to city B at a speed of 70 kmph and from city B to city C at 30 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? Pick one:
A) kmph
B) kmph
C) kmph
D) kmph
E) kmph

Solution: Let the distances between city A to B and B to C be 2x km and 3x km respectively.   Total time taken to cover from A to C   = (2x)/70 + (3x)/30   = (6x + 21x)/210 = 27x/210   = x/10 Average speed   = (2x + 3x)/(27x/210) = 38.9 kmph.   Answer: kmph
Answer: B
The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 40 years, was replaced by a new person. Find the age of the new person?  Pick.
A) 18  B) 56  C) 12  D) 17  E) 10

Solution: Initial average age of the 10 persons be P.   Age of the new person Q.   Sum of the ages of the initial 10 persons = 10P   New average   = (P-3) 10(P-3)   = 10P - 40 + Q   => Q = 10   Answer:10
Answer: E
A jet plane is rising vertically with a velocity of 10 m/s. It has reached a certain height when the pilot drops a coin, which takes 4 sec to hit the ground. Assuming that there is no resistance to the motion of the coin, the height of the place and the velocity of the coin on impact with the ground are:
Choose the correct answer
A) 38.4 m, 28.7 m/s B) 38.4 m, 29.2 m/s C) 26.5 m, 13.5 m/s D) 26.5 m, 28.7 m/s E) 26 m

Solution: The coin will move up with the initial velocity of 10 m/s till it comes to rest. Time taken is given by:   0=10âˆ’9.8t   â‡’t=10/9.8 sec.   Time taken to reach the ground from the highest point:   =4âˆ’10/9.8   =29.2/9.8 sec   Velocity of coin on impact   =0+9.8Ã—(29.2/9.8)   =29.2 m/s   If 'h' is the height from which the coin dropped.   Then   29.2^2âˆ’10^2=2Ã—9.8Ã—h   â‡’h = 38.4 m   Answer : 38.4 m, 29.2 m/s
Answer: B
A man visits a shopping mall almost every day and he walks up an up-going escalator that connects the ground and the first floor. If he walks up the escalator step by step it takes him 16 steps to reach the first floor. One day he doubles his stride length (walks up climbing two steps at a time) and it takes him 12 steps to reach the first floor.
Choose the correct choice from the following answers:	A) 15	B) 16	C) 47	D) 48	E) 49

Solution: Let d be the distance traveled, which remains same in both the cases. if v is the speed of the man and x is the speed of elevator, in case 1 the number of steps taken is   d/v+x=16   In case 2 it is   d/2v+x=12   because now he is traveling at double the speed; eliminating d, we get x=2v; therefore d=48v; when stationery x=0, we get no. of steps as 48v/v=48.   ANSWER:48
Answer: D
The product of two numbers is 168 and the sum of these two numbers is 26. What is the largest of these two numbers?
Choose the correct answer:  A) 12  B) 14  C) 16  D) 18  E) None of these

Solution: Explanation:   Let the numbers be x and (26 – x) .   Therefore,   x (26 – x) = 168   x2 – 26x + 168 = 0   (x – 14) (x – 12) = 0   x = 14 or x = 12   So, the numbers are 14 and 12.   ANSWER: 14
Answer: B
A can run a kilometer race in 4 1/2 min while B can run same race in 5 min. How many meters start can A give B in a kilometer race, so that the race mat end in a dead heat?  Answers
A) 288  B) 266  C) 155  D) 100  E) 112

Solution: A can give B (5 min - 4 1/2 min) = 30 sec start.   The distance covered by B in 5 min = 1000 m.   Distance covered in 30 sec = (1000 * 30)/300= 
(1000 * 30)/300 = 100
100 m.   A can give B 100m start.   Answer:100
Answer: D
The value of X+3X(5X)(X)when X =2 is:	Pick.
A) 132 B) 120 C) 122 D) 108 E) 123

Solution: Solution:   X+3X(5X)(X)   Put the value of X= 2 in the above expression we get,   2+ 6(2 x 5)(2)   = 2+ 6(10)(2)   = 2 + 120= 
2 + 120 = 122
122   Answer :122
Answer: C
Who is second to the right of H?
Select.
A) 67  B) 88  C) 166  D) 19  E) 911

Solution: Answer: Option 88
Answer: B
The banker's discount on Rs.1800 at 8% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?	Select the correct option
A) 3 months
B) 4 months
C) 5 months
D) 6 months
E) 7 months

Solution: Solution   S.I on Rs.1800 = T.D on Rs.1872.   P.W on Rs.1872 is Rs.1800.   Rs.72 is S.I on Rs. 1800 at 8%.   Time	=(100x72 / 8x1800)   = 1/2 year   = 6 months.   Answer 6 months
Answer: D
If p+5/q is a prime integer, which of the following must be true?
1.q=5p
2.q is a prime integer
3. p+5/q is ODD.  Select the correct option
A) None
B) 1 only
C) 2 only
D) 1 and 2 only
E) 2 and 3 only.

Solution: I would pick up numbers and do .   i hope the question is (p+5)/q....   let p = 3 , q = 4   3+5/4 = 2 = Prime   1. q is not equal to 5p   2.q is not a prime number   3. (p+5)/q is not odd.   hence None
Answer: A
A train speeds past a pole in 15 sec and a platform 120 m long in 25 sec, its length is?  Pick one.
A) 50 m  B) 180 m  C) 200 m  D) 300 m  E) None of these

Solution: Let the length of the train be x m and its speed be y m/sec.   Then, x/y = 15 => y = x/15   (x + 120)/25 = x/15 => x = 180 m.   ANSWER:180 m
Answer: B
The mean of 50 observations was 41. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is
Select the correct option: A) 35.2 B) 36.1 C) 36.5 D) 41.5 E) None

Solution: Sol.   Therefore correct sum   = ( 41 × 50 + 48 – 23)   = 2075.   Therefore correct mean   = 2075 / 50   = 41.5.   Answer 41.5
Answer: D
A letter lock consists of three rings each marked with five different letters. The number of distinct unsuccessful attempts to open the lock is at the most?	Choose the most appropriate option:
A) 176	B) 124	C) 215	D) 197	E) 172

Solution: Since each ring consists of five different letters, the total number of attempts possible with the three rings is   = 5 * 5*5= 
5 * 5*5 = 125
125. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 125 - 1= 
125 - 1 = 124
124.   Answer: 124
Answer: B