MU-NLPC/Calc-aqua_rat huggingface dataset:
A company assigns product codes consisting of all the letters in the alphabet.How many product codes are possible if the company uses at most 5 letters in its codes, and all letters can be repeated in any one code?
Choices:
A) A.15600
B) B.1622654
C) C.12356630
D) D.24515230
E) E.28572218

Solution: The no of ways in which the company can make codes of 1 letter : 26   # for 2 letters :   26*26= 
  26*26 = 676
676   # for 3 letters :   26 * 26*26= 
  26 * 26*26 = 17_576
17576   # for 4 letters :   26 * 26*26*26= 
  26 * 26*26*26 = 456_976
456976   # for 5 letters :   26 * 26*26*26*26= 
  26 * 26*26*26*26 = 11_881_376
11881376   The total : By adding all of them , 26+676+17576+456976+11881376=12356630   C.12356630
Answer: C
The food in a camp lasts for 40 men for 40 days. If ten more men join, how many days will the food last? Select
A) 40 days	B) 20 days	C) 32 days	D) 50 days	E) 45 days

Solution: one man can consume the same food in 40*40= 
40*40 = 1_600
1600 days.   10 more men join, the total number of men= 50   The number of days the food will last = 1600/50= 
1600/50 = 32
32 days.   ANSWER:32 days
Answer: C
How many positive integers less than 100 have a reminder 5 when divided by 7?	Choose the correct choice from the following:
A) 11 B) 12 C) 13 D) 14 E) 15

Solution: take the multiples of 7 and add 5   0X7+5=5 ....13X7+5=96   there are 14 numbers   answer 14
Answer: D
If w and y are both odd prime numbers and w < y, how many distinct positive integer factors does 2wy have? Choose the correct option: A) 3 B) 4 C) 6 D) 8 E) 12

Solution: Since 2wy prime factors are w^1*y^1*2^1, its total number or factors must be (1+1)(1+1)(1+1)=2^3=8. Thus, I think 8 would be the correct answer.8
Answer: D
A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 8 minutes less than they can row it in still water. How long would they take to row down with the stream  Choose one.
A) 45 or 23 minutes B) 63 or 12 minutes C) 76 minutes D) 19 minutes E) 25 minutes

Solution: A method has been discussed here to nullify the calculations though.   All I can input here is,   speed of a crew in still water = 1/2 ( speed upstream + speed downstream)   approximating this for time,   t = 1/2(84+ (t-8))   giving t = 76   76 minutes.
Answer: C
In an engineering class that contained 150 students, the final exam consisted of 2 questions. Three fifths of the students answered the first question correctly. If four fifths of the remainder answered the second question correctly, how many students answered both questions incorrectly?  Choose the correct choice from the following answers:
A) 4
B) 6
C) 10
D) 12
E) 24

Solution: 1st Question : Three fifths of the students answered the first question correctly - so 3/5âˆ—150=90   2nd Question : four fifths of the remainder answered the second question correctly so 4/5âˆ—(150âˆ’90)=4/5âˆ—60=48   total students who answered at least one Q correct =90+48= 
90+48 = 138
138   so students who answered BOTH incorrectly= 150âˆ’138=12   ANSWER:12
Answer: D
A train 500 m long, running with a speed of 180 km/hr will pass a tree in?	Choose one:	A) 17 sec	B) 16 sec	C) 18 sec	D) 10 sec	E) 12 sec

Solution: Speed = 180 * 5/18= 
180 * 5/18 = 50
50 m/sec   Time taken= 500 * 1/50= 
500 * 1/50 = 10
10 sec   Answer: 10 sec
Answer: D
When tossed, a certain coin has equal probability of landing on either side. If the coin is tossed 4 times, what is the probability that it will land twice on heads and twice tails?  Choose the correct choice from the following choices
A) 1/8  B) 1/4  C) 1/16  D) 1/32  E) 1/2

Solution: Must be twice on heads and twice on tails   1/2*1/2*1/2*1/2 = 1/16   Answer: 1/16
Answer: C
Two numbers are in ratio P:Q. when 1 is added to both the numerator and the denominator, the ratio gets changed to R/S. again, when 1 is added to both the numerator and denominator, it becomes 1/2. Find the sum of P and Q. Choose the correct choice from the following answers:	A) 3	B) 4	C) 5	D) 6	E) 7

Solution: Solution: If we go through normal method, It will be quite cumbersome,so,   We will solve this question through options.   Taking option a: It has P+Q = 3. The possible value of P/Q is 1/2 or 2/1.   Using 1/2, we see that on adding 2 in both the numerator and denominator we get 3/4 (not required value.   Similarly we check for 2/1, this will also not give the required value.   OPTION b:   We have 1/3 possible ratio.   Then, we get the final value as 3/5 (not = to 1/2)   Hence, rejected.   Here we have 1/4 or 2/3.   Checking for 1/4 we get 3/6 = 1/2. Hence, the option is correct.   Option c:
Answer: C
An alloy is to contain copper and zinc in the ratio 9:4. The zinc required to be melted with 24kg of copper is?
Select the correct option:
A) 12kg
B) 8.3kg
C) 10.7kg
D) 15.5kg
E) 7kg

Solution: Let the required quantity of copper be x kg   9:4::24:x   9x = 4*24   x = 10 2/3 kg = 32/3 = 10.7kg   Answer is 10.7kg
Answer: C
The speed of a car is 90 km in the first hour and 55 km in the second hour. What is the average speed of the car?
Choose the correct choice from the following:
A) 72.5 kmph
B) 75 kmph
C) 87 kmph
D) 56 kmph
E) 86 kmph

Solution: S = (90 + 55)/2= 
(90 + 55)/2 = 145/2 = around 72.5
72.5 kmph   72.5 kmphnswer: 72.5 kmph
Answer: A
Find the sum 3/10 + 5/100 + 8/1000 in decimal form ?  Pick.
A) 0.853  B) 0.358  C) 3.58  D) 8.35  E) None

Solution: Answer   3/10 + 5/100 + 8/1000   = 0.3 + 0.05 + 0.008= 
0.3 + 0.05 + 0.008 = 0.358
0.358   Correct Option: 0.358
Answer: B
Two numbers are respectively 50% and 100% more than a third number. The percentage that is first of the second is? Choose the correct option:
A) 65% B) 83% C) 27% D) 42% E) 75%

Solution: I II III   150 200 100   200----------150   100-----------? => 75%   Answer:75%
Answer: E
If 5 shirts can be purchased for 5 dollars, how many shirts can be purchased for 7 dollars?  Pick one:
A) 5
B) 8
C) 7
D) 1
E) 2

Solution: 5*7= 
5*7 = 35
35;    35/5= 
 35/5 = 7
7   Ans= 2
Answer: E
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?  Select the correct option.
A) 2 years
B) 4 years
C) 5 years
D) 6 years
E) 7 years

Solution: Mother's age when Ayesha's brother was born = 36 years.   Father's age when Ayesha's brother was born = (38 + 4)= 
(38 + 4) = 42
42 years.   Required difference= (42 - 36)= 
(42 - 36) = 6
6 years.   answer :6 years
Answer: D
One type of liquid contains 25 % of benzene, the other contains 30% of benzene. A can is filled with 6 parts of the first liquid and 4 parts of the second liquid. Find the percentage of benzene in the new mixture.  Choices
A) 28 %  B) 25 %  C) 30 %  D) 27%  E) 32%

Solution: Let the percentage of benzene =X   (30 - X)/(X- 25) = 6/4 = 3/2   => 5X = 135 or   X = 27 so,   required percentage of benzene = 27 %   ANSWER:27%
Answer: D
There is a escalator and 2 persons move down it.A takes 50 steps and B takes 75 steps while the escalator is moving down.Given that the time taken by A to take 1 step is equal to time taken by B to take 3 steps.Find the no. of steps in the escalator while it is staionary?	Choose the correct choice
A) 60  B) 70  C) 80  D) 90  E) 100

Solution: If A takes 1 step in one second, then B takes 3 steps in one second. If A takes t1 seconds to   take 50 steps, then B takes 150 steps in t1 seconds.   For B, to take 150 steps he requires t1 seconds,   then to take 75 steps he requires t1/2 seconds.   now use relative velocity   L - v*t1=50 (for first person)   L-v*t1/2=75(for second person)   S(escalator w.r.t ground)-s(person w.r.t escalator)=s1(person w.r.t ground)   S,s,s1 are the steps   now put the v*t1 from 1 into the second equation and u get   L- (L-50)/2=75   L+50=150   L=100   ANSW100R:100
Answer: E
Find avrg speed if a man travels at speed of 15km/hr up and 28km/hr dawn at an altitude of 230m. Select the correct option:
A) 25.8  B) 19.5  C) 18.0  D) 12.2  E) 29.8

Solution: avg speed=2*x*y/(x+y)   =2*15*28/(15+28)=19.5   ANSWER:19.5
Answer: B
If a farmer is splitting her crop of apples between her nine customers, how many would be left if she evenly divided the 541 apples?	Choices:
A) 1
B) 3
C) 5
D) 6
E) 9

Solution: If a number is divisible by 9, the sum of its digits must be a multiple of 9.   Here,5+4+1=10. This means 1 apple will remain after the rest are divided among the nine customers.   1
Answer: A
A sum of money becomes triple itself in 4 years at simple interest. How many years will it become six times at the same rate? Options:  A) 11 years  B) 10 years  C) 12 years  D) 14 years  E) 16 years

Solution: 100 ---- 200 ---- 4   200 ---- 4   100 ---- 2   ------------------   600 ---- 10 years   ANSWER:10 years
Answer: B
If a company allocates 10 percent of its budget to advertising, 10 percent to capital improvements, and 5 percent to salaries, what fraction of its budget remains for other allocations?
Choose the correct choice from the following answers
A) 1/4  B) 2/4  C) 3/4  D) 1/5  E) 2/5

Solution: 100%-(10%+10%+5%)=75% remains for other allocations --> 75% 100 -(10 +10 +5 )= 
100 -(10 +10 +5 ) = 75
75% remains for other allocations --> 75% = 75/100   --  75= 
  --  75 = 75
75/100= 3/4.   Answer: 3/4.
Answer: C
If the average of 10 digits is 80 and the average of 6 of them is 58, calculate the average of the remaining 4 numbers?
Choose the correct choice from the following: A) 119 B) 117 C) 116 D) 113 E) 115

Solution: Explanation:   Total of the 10 digits - 10*80 = 800   Total of the 6 digits - 6*58 = 348   Total of the remaining 4 digits - 800-348 = 452   average of the remaining 4 numbers = 452/4= 
452/4 = 113
113   ANSWER: 113
Answer: D
Find the C.I. on a sum of Rs.1600 for 9 months at 20% per annum, interest being compounded quarterly?	Pick one
A) 3388  B) 2778  C) 2522  D) 2988  E) 2771

Solution: A = 1600(21/20)3 = 2522   Answer:2522
Answer: C
A company seeks to hire a sales manager, a shipping clerk, and a receptionist. The company has narrowed its candidate search and plans to interview all remaining candidates including 7 persons for the position of sales manager, 6 persons for the position of shipping clerk, and 10 persons for the position of receptionist. How many different hirings of these three people are possible?  Choose the correct option:
A) 7 + 6 + 10  B) 7 × 6 × 10  C) 21 × 20 × 19  D) 7! + 6! + 10!  E) 7! × 6! × 10!

Solution: 1 sales manager can be selected out of 7 in 7 ways   1 clerk can be selected out of 6 in 6 ways   1 receptionist can be selected out of 10 in 10 ways   total no. of ways these 3 can be selected = 7 *6 * 10   Ans. 7 × 6 × 10) 7 × 6 × 10
Answer: B
John had $100 to buy drinks and sandwiches for his birhtday party. He bought 5 small boxes of drinks at $4 each box and 8 boxes of sandwiches at $6 each box. How much money was left after the shopping? Choose the correct choice from the following answers:  A) $32  B) $33  C) $34  D) $35  E) $36

Solution: Money spent on drinks   5 * 4= 
5 * 4 = 20
$20   Money spent on sandwiches    8 * 6= 
 8 * 6 = 48
$48   Total money spent     20 + 48= 
  20 + 48 = 68
$68   Money left after shopping    100 - 68= 
 100 - 68 = 32
$32   correct answer $32
Answer: A
If 20% of a = b, then b% of 20 is the same as : Answers
A) 4% of a	B) 8% of a	C) 12% of a	D) 9% of a	E) 1% of a

Solution: 20% of a = b   b% of 20 = = = = 4% of a.   4% of answer: a
Answer: A
Find the length of the wire required to go 15 times round a square field containing 69696 m2? Choose the correct choice from the following choices
A) 15840  B) 19879  C) 27997  D) 15842  E) 15823

Solution: a2 = 69696 => a = 264   4a = 1056   1056 * 15= 
1056 * 15 = 15_840
15840   15840nswer:15840
Answer: A
A set of numbers contains 7 integers and has an average (arithmetic mean) value as well as a median value of 23. If the largest value is equal to 15 more than 4 times the smallest number, what is the largest possible range for the numbers in the set?
Choose the correct choice from the following
A) 33 B) 35 C) 38 D) 48 E) 75

Solution: The average of 7 numbers is 23 --> the sum of these numbers is 7*23= 
7*23 = 161
161;   The median of 7 numbers is 23 --> 23 is the middle term: {*, *, *, 23, *, *, *};   The largest value is equal to 15 more than 4 times the smallest number --> say the smallest number is x then the largest number would be 4x+15, so our set is {x, *, *, 23, *, *, 4x+15};   Now, in order to maximize the range we need to make the second and the third numbers equal to x and the fifth and sixth numbers equal to 23, so the set should be {x, x, x, 23, 23, 23, 4x+15}.   Since the sum is 161 then x+x+x+23+23+23+4x+15=161 --> x=11.   The range is (4x+15)-x=3x+15=48.   Answer: 48.
Answer: D
A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. If the smaller wheel has made 21 revolutions, what will be the number of revolutions made by the larger wheel?
Choices
A) 15  B) 12  C) 21  D) 9  E) 22

Solution: Explanation:   Let the number of revolutions made by the larger wheel be x   More cogs, less revolutions (Indirect proportion)   Hence we can write as   (cogs) 6 : 14 :: x : 21   ⇒6×21=14 × x   ⇒6×3=2 × x   ⇒3×3 = x   ⇒x = 9   Answer: Option 9
Answer: D
If the average (arithmetic mean) of a and b is 100, and the average of b and c is 160, what is the value of a − c?  Choose one
A) −120	B) −100	C) 100	D) 135	E) It cannot be determined from the information given

Solution: Question: a - c = ?   (a + b)/ 2 =100 ===> a + b = 200   (b + c)/2 = 160 ===> b + c = 320   (a + b) - (b + c) = 200 - 320 ===> a + b - b - c = - 120 ===> a - c = - 120   −120nswer: −120
Answer: A
A and B can do a work in 12 days, B and C in 30 days and C and A in 36 days. In how many days will the work be completed, if all three of them work together? Choices:
A) 180/15  B) 180/10  C) 180/13  D) 180/15  E) 180/11

Solution: One day work of A and B = 1/12   One day work of B and C = 1/30   One day work of C and A = 1/36   2(A + B + C) = 1/12 + 1/30 + 1/36   2(A + B + C) = 13/90   (A + B + C) = 13/180   Number of days required = 180/13 days.   Answer: 180/13
Answer: C
A, B and C started a business with a total investment of Rs. 72000. A invests Rs. 6000 more than B and B invests Rs. 3000 less than C. If the total profit at the end of a year is Rs. 8640, Find C's share. Choose one.
A) Rs. 3240	B) Rs. 2520	C) Rs. 2880	D) Rs. 3360	E) None of these

Solution: Explanation:   Let C's investment = Rs. x   B's investment = Rs. (x - 3000)   A's investment = Rs. (x - 3000 + 6000) = Rs. (x + 3000)   Now, (A + B + C)'s investment = Rs. 72000   => x + (x - 3000) + (x + 3000) = 72000   => 3x = 72000   => x = 24000   Hence, A's investment = Rs. 27000   B's investment = Rs. 21000   C's investment = Rs. 24000   Ratio of the capitals of A, B and C   = 27000 : 21000 : 24000   = 9 : 7 : 8   A's share = Rs. [(8/24) Ã— 8640] = Rs. 2880   Answer: Option Rs. 2880
Answer: C
A work crew of 4 Men takes 5 days to complete one-half of a job. If 11 men are then added to the crew and the men continue to work at the same rate, how many days will it take the enlarged crew to do the rest of the job? Choose the correct choice from the following options
A) 2
B) 3
C) 1 1/3
D) 4
E) 4 4/5

Solution: Suppose 1 man can do work in X days..   so 4 men will do in ..   4/X=1/5*1/2 as half job is done   X=40   now 11 more are added then   15/40=1/2*1/d for remaining half job   d=1 1/3 Number of days   1 1/3
Answer: C
The remainder when 1!+2!+3!...+50! divided by 6! will be
Choose the most appropriate option:
A) 21
B) 153
C) 77
D) 927
E) 19

Solution: The remainder when the terms greater than 6! are divided by 6! becomes 0 so we need to consider the terms upto 5!.   So remainder will be whatever is obtained by dividing 1!+2!+3!+4!+5! with 6!.   So remainder is obtained by dividing  (1+2+6+24+120)= 
 (1+2+6+24+120) = 153
153 with 6! ( 720)   So remainder is 153.   Answer:153
Answer: B
The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 128,000 locusts?  Options.
A) 12
B) 8
C) 4
D) 10
E) 16

Solution: - 4 hours: 1,000   -2 hours: 2,000   Now: 4,000   + 2 hours: 8,000   + 4 hours: 16,000   + 6 hours: 32,000   + 8 hours: 64,000   + 10 hours: 128,000   Answer : 10
Answer: D
Find the face value of 5 in 358946
Choose the correct answer
A) 50
B) 5
C) 500
D) 5000
E) 50000

Solution: Face value is the value of digit itself   face value of 5 = 5   Answer : 5
Answer: B
Rich has 3 green, 2 red and 3 blue balls in a bag. He randomly picks 5 from the bag without replacement. What is the probability E that of the 5 drawn balls, Rich has picked 1 red, 2 green, and 2 blue balls?  Choose the correct choice from the following choices.
A) 8/28  B) E=9/28  C) 10/28  D) 10/18  E) 11/18

Solution: (3c2*2c1 *3c2)/8c5   =(3*2*3)/(8*7*6/3*2)   =18/56   =9/28   E=9/28
Answer: B
Find the value of (200+ 200/90) × 90  Pick one.
A) 18500  B) 18200  C) 17500  D) 16500  E) 13500

Solution: (18000 + 200)/90 * 90= 
(18000 + 200)/90 * 90 = 18_200
18200   Answer : 18200
Answer: B
Three years ago the average age of a family of six members was 19 years. A boy have been born, the average age of the family is the same today. What is the age of the boy? Choices
A) 1	B) 2	C) 7	D) 3	E) 8

Solution: 6 * 22= 
6 * 22 = 132
132   7 * 19= 
7 * 19 = 133
133   --------------   1   1nswer: 1
Answer: A
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 26 seconds, what is the ratio of their speeds? Pick
A) 1:3	B) 9:1	C) 2:3	D) 3:2	E) 3:4

Solution: Let the speed of the trains be x and y respectively   length of train1 = 27x   length of train2 = 17y   Relative speed= x+ y   Time taken to cross each other = 26 s   = (27x + 17 y)/(x+y) = 26   = (27x + 17 y)/ = 26(x+y)   = x = 9y   =x/y = 9/1   Answer :9:1
Answer: B
Three years ago the average age of a family of nine members was 23 years. A boy have been born, the average age of the family is the same today. What is the age of the boy? Select the correct option.
A) A)4 B) B)5 C) C)6 D) D)7 E) E)8

Solution: 9 * 26= 
9 * 26 = 234
234   10 * 23= 
10 * 23 = 230
230   --------------   4   4nswer: 4
Answer: A
If a and b are different positive integers and a + b = b(a + b), then which of the following must be true?
I. b = 1
II. a = 1
III. b < a	Choose the correct choice from the following answers.
A) I only B) II only C) III only D) I and II E) I and III

Solution: b has to equal a squared, and that only works if b is 1. There are no positive integers less than 1, so I and III are correct.   Answer : I and III
Answer: E
The average weight of 20 persons sitting in a boat had some value. A new person added to them whose weight was 49 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 20 persons? Select the correct option:
A) 55  B) 56  C) 57  D) 58  E) 59

Solution: 20x + 49 = 21(x – 5)   X=56   ANSWER:56
Answer: B
The surface of a cube is 24sq cm. Find its volume?
Choose one:
A) 8
B) 6
C) 4
D) 3
E) 1

Solution: 6a2 = 24   a = 2 => a3 = 8cc   8nswer: 8
Answer: A
A sum of Rs.13000 is divided into three parts such that the simple interests accrued on them for two, three and four years respectively may be equal. Find the amount deposited for 4 years. Choose the correct choice:
A) 5000  B) 6000  C) 4000  D) 3000  E) 7000

Solution: Let the amounts be x, y, z in ascending order of value. As the interest rate and interest accrued are   same for 4 years 3 years and 2 years i.e. 4x = 3y = 2z = k.   L.C.M. of 4,3,2 = 12 So x:y:z: = 3000 : 4000 :6000   The amount deposited for 4 years = 3000   ANSWER:3000
Answer: D
The sum of the present ages of A, B, C is 57 years. Three years ago their ages were in the ratio 1:2:3. What is the present age of A?
Pick one:
A) 8
B) 9
C) 10
D) 11
E) 12

Solution: Three years ago:   a:b:c = 1:2:3   Let a = 1x, b = 2x, and c = 3x.   Today:   (x+3) + (2x+3) + (3x+3) = 57   x = 8   So the present age of A is x+3 = 11   The answer is 11.
Answer: D
Find four consecutive even integers so that the sum of the first two added to twice the sum of the last two is equal to 754.
Choose the correct choice from the following:
A) 122 , 124 ,126, 128 B) 120 ,122 , 124 ,128 C) 120 ,121 , 122 ,123 D) 123 ,125 , 127 ,129 E) None of these

Solution: Let x, x + 2, x + 4 and x + 6 be the four integers. The sum of the first two   x + (x + 2)   twice the sum of the last two is written as   2 ((x + 4) + (x + 6)) = 4 x + 20   sum of the first two added to twice the sum of the last two is equal to 754 is written as   x + (x + 2) + 4 x + 20 = 754   Solve for x and find all four numbers   x = 122 , x + 2 = 124 , x + 4 = 126 , x + 6 = 128   122 , 124 ,126, 128nswer 122 , 124 ,126, 128
Answer: A
Six years ago Anita was P times as old as Ben was. If Anita is now 17 years old, how old is Ben now in terms of P ?	Choose the correct choice from the following answers
A) 11/P + 6  B) 11/P + 9  C) 11/P + 5  D) 11/P + 3  E) 11/P + 1

Solution: Explanation:   Let Ben’s age now be B   Anita’s age now is A.   (11/P + 6 - 6) = P(B - 6)   But 11/P + 6 is 17 and therefore 11 = P(B - 6)   11/P = B-6   (11/P) + 6 = B   11/P + 6nswer: 11/P + 6) 11/P + 6
Answer: A
A camera lens filter kit containing 5 filters sells for $75.50. If the filters are purchased individually, 3 of them are priced at $7.35 each, 3 at $12.05 each, 1 at $12.50. The amount saved by purchasing the kit is what percent of the total price of the 5 filters purchased individually?
Choose the correct choice from the following options
A) 5.35% B) 6.35% C) 7.35% D) 8.35% E) 9.35%

Solution: Cost of kit = $75.50   If filters are purchased individually - $7.35*3 + $12.05*3 + $12.50 = $70.70   Amount saved = $75.50 - $70.70 = $4.80   Required %age 75.50 -  70.70= 
75.50 -  70.70 = 4.8
$4.80   Required %age= ($4.80/$75.50)*100 = 6.35%   So, the correct answer is 6.35%.
Answer: B
If the perimeter of a rhombus is 52 cm and one of its
diagonals is 24 cm, then the area of the rhombus is	Choose the correct choice from the following answers.
A) 100 sq.cm
B) 110 sq.cm
C) 120 sq.cm
D) 130 sq.cm
E) 140 sq.cm

Solution: perimeter of rhombus = 4a (with side a)   4a=52 then a=13,   lets length of one diagonal p=24cm,   lenght of other diagonal is q;   area of rhombus = pq/2   using pythogorus theorem a^2= (p/2)^2 + (q/2)^2   we will get q=10.   then area=10*24/2= 
10*24/2 = 120
120 sq.cm   ANSWER:120 sq.cm
Answer: C
A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most
Choose the correct choice.
A) 238  B) 377  C) 215  D) 287  E) 162

Solution: Explanation:   Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6= 
6 * 6 * 6 = 216
216. Of these attempts, one of them is a successful attempt.   Maximum number of unsuccessful attempts= 216 - 1= 
216 - 1 = 215
215.   Answer: 215
Answer: C
An accurate clock shows 8 o'clock in the morning. Through how may degrees will the hour hand rotate when the clock shows 2 o'clock in the afternoon? Choose the correct choice from the following answers:
A) 180 B) 345 C) 234 D) 488 E) 234

Solution: Angle traced by the hour hand in 6 hours = (360)/12x 6º	= 180º.   180nswer:180
Answer: A
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age was five times the age of the son. After 6 years, son's age will be:  Choose the most appropriate option.
A) 5:2
B) 7:3
C) 9:2
D) 13:4
E) 3:4

Solution: Let the age of father and son 10 years ago be 3x and x years respectively.   Then, (3x + 10) + 10 = 2[(x + 10) + 10]   3x + 20 = 2x + 40 => x = 20.   Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3   ANSWER:7:3
Answer: B