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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 student got twice as many sums wrong as he got right. If he attempted 48 sums in all, how many did he solve correctly ?

  • 12
  • 16
  • 24
  • 18

Answer: Option B

Explanation:

Suppose boy got x sums right and 2x sums wrong,
then,
x+2x = 48
=> 3x = 48
=> x = 16

2. 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.

3. Reena is twice as old as Sunita. Three years ago, she was three times as old as Sunita. How old is Reena now ?

  • 6 years
  • 12 years
  • 14 years
  • 16 years

Answer: Option B

Explanation:

Let Sunita's present age = x years
Then Reena present age = 2x years

Three years ago
(2x-3) = 3(x-3)
2x - 3 = 3x - 9
or x = 6

Reena age = 2x = 2*6 = 12 year.

4. 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



5. In a class, there are 18 boys who are over 160 cm tall. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class ?

  • 10
  • 12
  • 14
  • 18

Answer: Option B

Explanation:

Let the number of boys be x.
Then, 3/4 x = 18
=> x = 24

If total number of students is y, then
2/3 y = 24
=> y = 36

Number of girls in class = y - x
= 36 - 24 = 12

Read more from - Arithmetic Reasoning Questions Answers
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