### Problems on Numbers Questions and Answers

#### Article

Q 1

There are 3 persons Sudhir, Arvind, and Gauri. Sudhir lent cars to Arvind and Gauri as many as they had already. After some time, Arvind gave as many cars to Sudhir and Gauri as many as they have. After sometime Gauri did the same thing. At the end of this transaction each one of them had 24. Find the Sudhir originally had.

A)

21

B)

30

C)

35

D)

39

Correct Option - D

Explanation

S             A            G

24           24          24

12           12          48

6             42          24

39           21          12

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Q 2

A, B, C are having some marbles with each of them. A has given B and C the same number of marbles each of them already have. Then, B gave C and A the same number of marbles they already have. Then C gave A and B the same number of marbles they already have. At the end A, B, and C have equal number of marbles. If x, y, z are the marbles initially with A, B, C respectively. If the total number of marbles are 72, then the number of marbles with A at the starting

A)

20

B)

30

C)

32

D)

39

Correct Option - D

Explanation

A - (x-y-z)

B - 2y

C - 2z

B gives A and C

A - 2(x-y-z)

B - 2y-(x-y-z+2z) = 3y-x-z

C - 4z

C gives A and B

A - 4(x-y-z)

B - 2(3y-x-z)

C - 4z-(2x-2y-2z+3y-x-z) = 7z-x-y

4(x-y-z) = (6y - 2x - 2z) = (7z - x - y)

Sum of these three terms is 72.

Solving these equations, x=39.

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Q 3

How many 9 digit numbers are possible by using the digits 1, 2, 3, 4, 5 which are divisible by 4 if repetition is allowed?

A)

5^7

B)

5^6

C)

5^9

D)

5^8

Correct Option - D

Explanation

The last two digits can take 5 values.

12, 24, 32, 44, 52

The first seven digits can be any one of the 5 numbers.

No. of ways = 5^7

Total no. of ways

5^7 * 5 = 5^8

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Q 4

A man divides Rs.8600 among 5 sons, 4 daughters and 2 nephews. If each daughter receives four times as much as each nephew, and each son receives five times as much as each nephew, how much does each daughter receive?

A)

Rs.800

B)

Rs.600

C)

Rs.200

D)

Rs.700

Correct Option - A

Explanation

5s+4d+2n=8600

d=4n

s=5n

25n+16n+2n=8600

43n=8600

n=200

d=800

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Q 5

The difference between two numbers is 9 and the product of the two is 14. What is the square of their sum?

A)

109

B)

130

C)

137

D)

145

Correct Option - C

Explanation

x-y=9

xy=14

(x-y)²=x²+y²-2xy

81 = x²+y²-28

x²+y²=109

(x+y)² = x²+y²+2xy

= 137

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Q 6

Of the two-digit numbers (those from 11 to 95, both inclusive) how many have a second digit greater than the first digit?

A)

37

B)

38

C)

36

D)

35

Correct Option - C

Explanation

8 numbers from 12 to 19

7 from 23-29

6 from 34-39

5 from 45-49

4 from 56-59

3 from 67-69

2 from 78-79

1 - 89

Total - 36

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Q 7

Ria has a jewel chest containing Rings, Pins and Ear-rings. The chest contains 26 pieces. Ria has 2 1/2 times as many rings as pins, and the number of pairs of earrings is 4 less than the number of rings. How many earrings does Ria have?

A)

12

B)

8

C)

6

D)

10

Correct Option - A

Explanation

Let e be the number of pairs of earrings.

r+p+2e=26

r=2.5p

e=r-4 = 2.5p-4

2.5p+p+5p-8=26

8.5p = 34

p=4

e=2.5p - 4 = 6

6 pairs of earrings. 12 ear rings.