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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. 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 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 = 3x5 and son's age x5
So, 3x5 = 4(x5)
=> 3x5 = 4x20
=> x = 15
3. I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ?
 25
 37
 54
 65
Answer: Option A
Explanation:
The required number will be such that it leaves a reminder of 1 when divided by 2, 3 or 4 and no reminder when divided by 5. Such a number is 25 among options
4. 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
(2x3) = 3(x3)
2x  3 = 3x  9
or x = 6
Reena age = 2x = 2*6 = 12 year.
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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