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

Answer: Option A

Explanation:

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

2. The number of boys in a class is three times the number of girls. Which one of the following numbers cannot represent the total number of children in the class ?

Answer: Option C

Explanation:

Let number of girls = x and number of boys = 3x.

Then, 3x + x = 4x = total number of students.

Thus, to find exact value of x, the total number of students must be divisible by 4.

3. 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 ?

Answer: Option B

4. 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 :

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

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