1. A fruit vendor has to arrange some number of fruits in rows. When he put five fruits in each row he

was left with one fruit . Then he tried six fruits in a row, then 8 , then 9, then 12. But always he was left

with one fruit . so he thought for a while and put 13 fruits in a row and then he was left with none . what

is the smallest number of fruits ?

1)3601 2)6301 3)2601 4)4601 5)None of these

Solution: (1).when 5 or 6 or 8 or 9 or 12 fruits are arra nged in rows, one fruit is left.

LCM ( 5,6,8,9,12 ) = 360

Then the number of fruits is 360x + 1 .

It is given , number of fruits perfectly divisible by 13

Then (360x + 1) / 13

Substitute x = 1

= (360 x 1 +1 ) / 13

X = 2,3,4 , ………………..

X = 10

(360 x 10 + 1) / 13

is perfectly divisible

= 3601 / 13 = perfectly divisible

Alternately :

Among the options only first option is perfectly divisible by 13

2. What is the LCM of (m+1) (m+5) (m-3)2 and (m-3) (m+1)3 (m+5)2

1).(m+5) (m+1)(m-3) 2).(m+5)2 (m+1)3 (m-3)2

3).(m+5)(m+1) 4).(m+5)2 (m+1) (m-3)

5)None of these

Solution: (2). LCM [ (m+1) (m+5) (m-3)2, (m-3)(m+1)3(m+5)2 ]

Consider all greater powers

Ans = (m+5)2 (m+1)3 (m-3)2

3. If the LCM of A & B is C . Find their HCF.

1) (ABC)2 2) ABC / AB 3) AB / C 4)Cannot be determined 5)none of these

Solution: (3). First Number = A

Second Number = B

Given LCM (A,B) = C

LCM x HCF = A x B

C x HCF = A x B

HCF = AxB / C hence answer is AB / C

4. Find the least number of tiles required to lay the floor of length 150 cm and width 125 cm .

1) 40 2) 20 3) 30 4) 25 5) None of these

Solution: (4).This sum is based on equal distribution then HCF (150,125) = 30

Hence Answer is 25

5. Find the greatest number of 5 digits which when divided by 3,5,8,12 have 2 as remainder .

1) 99999 2) 99958 3) 99960 4) 99962 5) None of these

Solution ; (5). LCM (3,,5,8,12) = 120

Then 120x+2 = max.5 digits

When x = 833

Then 120 x 833 +2

99960 + 2

Answer : 99962

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