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Find the least number which leaves a reminder of 3 when divided by 5, 6, 7 and 8, but leaves no reminder when divided by 9 ?

  • 1683
  • 1692
  • 1598
  • 1458

Answer: Option A

Explanation:

First of all, calculate LCM of 5, 6, 7 and 8 which is 840.
Suppose Number is K
then 840 * K + 3 is divisible by 9.
If K = 1, number = (840 × 1) + 3 = 843 which is not divisible by 9

If K = 2, number = (840 × 2) + 3 = 1683 which is divisible by 9

So 1683 is correct answer.

Similar Questions :

1. In a caravan, in addition to 50 hens, there are 45 goats and 8 camels with some keepers. If the total number of feet be 224 more than the number of heads in the caravan, the number of keepers is

  • 5
  • 8
  • 10
  • 15

Answer: Option D

Explanation:

Let the number of keepers be x.
Then, total number of feet = 2*50+4*45+4*8+2x
= 2x + 312

Total number of heads = 50+45+8+x = 103 + x
Now, (2x+312) = (103+x)+224
=> x = 15

2. If 100 cats kill 100 mice in 100 days, then 4 cats would kill 4 mice in how many days ?

  • 4 day
  • 10 day
  • 40 day
  • 100 day

Answer: Option D

3. Aruna cut a cake into two halves and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty grams in weight. If she has seven pieces of the cake in all with her, how heavy was the original cake ?

  • 240 gm
  • 220 gm
  • 225 gm
  • 250 gm

Answer: Option A

Explanation:

Seven pieces consist of 6 smaller equal pieces and one half cake piece.

Weight of each small piece = 20 gm
So, total weight of the cake = 2 (20 * 6) = 240 gm

4. At the end of a business conference the ten people present all shake hands with each other once. How many handshakes will there be altogether ?

  • 20
  • 45
  • 55
  • 90

Answer: Option B

Explanation:

Total number of handshakes =
9+8+7+6+5+4+3+2+1 = 45

5. A father is now three times as old as his son. Five years back, he was four times as old as his son. The age of the son is :

  • 12
  • 15
  • 18
  • 20

Answer: Option B

Explanation:

Let son's age be x then father's age is 3x
Five years ago, father's age = 3x-5 and son's age x-5
So, 3x-5 = 4(x-5)
=> 3x-5 = 4x-20
=> x = 15

Read more from - Arithmetic Reasoning Questions Answers
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