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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. A shepherd had 27 sheep. All but 10 died. How many he left with ?

  • 10
  • 15
  • 17
  • 27

Answer: Option A

Explanation:

"All but 10 died" means all except 10 died, so he is remained with 10 sheep.

2. 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

3. In a chess tournament each of six players will play every other player exactly once. How many matches will be played during the tournament ?

  • 12
  • 15
  • 30
  • 36

Answer: Option B

Explanation:

I. matches of first player with other 5 players
II. matches of second player with 4 players other than the first player
III. matches of third player with 3 players other than the first player and second player.
IV. matches of fourth player with 2 players other than the first player, second player and third player.
V. matches of fifth player with 1 player other than the first player, second player, third player and fourth player.

So total matches will be 5+4+3+2+1 = 15



4. In a group of 15 people, 7 read French, 8 read English while 3 of them read none of these two. How many of them read French and English both ?

  • 2
  • 3
  • 4
  • 5

Answer: Option B

5. A is three times as old as B. C was twice-as old as A four years ago. In four years' time, A will be 31. What are the present ages of B and C ?

  • 9, 46
  • 9, 50
  • 10, 46
  • 10, 50

Answer: Option B

Explanation:

As from the question we have,
A = 3B --- (i)
c - 4 = 2(A+4) ---(ii)

Also, A + 4 = 31
or A = 31-4 = 27

Putting A = 27 in (i) we get
B = 9
Putting A = 27 in (ii) we get
C = 50

Read more from - Arithmetic Reasoning Questions Answers