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Question Detail
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.
1. 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
2. A, B, C and D play a game of cards. A says to B. "If I give you 8 cards, you will have as many as C has and I shall have 3 less than what C has. Also if I take 8 cards from C, I shall have twice as many as D has." If B and D together have 50 cards, how many cards have A got?
 35
 37
 38
 40
Answer: Option D
Explanation:
If we read given question carefully, we get,
B+8 = C (i)
A8 = C3 (ii)
A+6 = 2D (iii)
B+D = 50 (iv)
Putting C = A 5 from (ii) into (i), we have :
B+8 = A5 or AB = 13 (v)
Putting D = 50B from (iv) and (iii), we have :
A+6 = 1002B or A+2B = 94 (vi)
Solving (v) and (vi), we get
B = 27 and A = 40
3. A is three times as old as B. C was twiceas 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 = 314 = 27
Putting A = 27 in (i) we get
B = 9
Putting A = 27 in (ii) we get
C = 50
4. A group of 1200 persons consisting of captains and soldiers is travelling in a train. For every 15 soldiers there is one captain. The number of captains in the group is ?
 70
 75
 80
 85
Answer: Option B
Explanation:
Generally we may commit mistake of dividing 1200/15.
But out of 16 persons there is one captain.
so, it will be 1200/16 = 75
5. 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.
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