Playing with Numbers Test

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Playing with Numbers Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

If N divided by 5 leaves a remainder of 3, then one's digit of N must be _____.

A
Either 3 or 6

B
Either 3 or 8

C
Either 8 or 1

D
Either 8 or 6

Solution

N leaves remainder 3 when divided by 5.
⇒(N−3) is divisible by 5.
⇒ One's digit of N−3 is either 0 or 5.
⇒ One's digit of N is either 3 or 8.
Question 2
1 / -0

Given that the number 67y19 is divisible by 9, where y is a single digit, what is the least possible value of y?

A
3

B
9

C
7

D
4

Solution

67y19 is divisible by 9 so sum of its digits is also divisible by 9 6 + 7 + y + 1 + 9 = 23 + y is divisible by 9.

So, least possible value of y = 4.
Question 3
1 / -0

A 3-digit number 'cba' is divisible by 3 if____.

A
a + 2b + c is divisible by 3

B
2a + b + c is divisible by 3

C
a + b + 2c is divisible by 3

D
a + b + c is divisible by 3
Question 4
1 / -0

In a division, the divisor is 12 times the quotient and 5 times the remainder, if the remainder is 48, then dividend is ______.

A
240

B
576

C
4800

D
4848

Solution

Remainder = 48
∴ Divisor =48 × 5=240
Quotient =240/12=20
∵ Dividend = Divisor × Quotient + Remainder = 240 × 20 + 48 = 4800 + 48 = 4848.
Question 5
1 / -0

Which of the following statements is INCORRECT?

A
All even natural numbers which are divisible by 3 are also divisible by 6.

B
If a natural number is divisible by 21, then it is divisible by both 3 and 7.

C
If AB × 4 = 192, then A + B = 10

D
A number of the form 14 N + 2 leaves the remainder 2 when divided by 7.
Question 6
1 / -0

How many 5-digit numbers of the form AABAA is divisible by 33?

A
1

B
3

C
0

D
infinite

Solution

We have AABAA is divisible by 33. So, it is divisible by both 3 and 11.
∴A + B + A - (A + A)=B is divisible by 11.
⇒B=0 Also, A+A+B+A+A=4A+B is divisible by 3.
⇒4A is divisible by 3 (∵B=0)
⇒A is divisible by 3
Hence,
possible values of A are 0, 3, 6, 9
But A can't be equal to zero.
∴ Number of possible 5-digit numbers are 3.

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Re-Attempt Weekly Quiz Competition

Playing with Numbers Test - 4

Result

Playing with Numbers Test - 4

Score

-

Rank

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SHARING IS CARING

Question 1

Either 3 or 6

Either 3 or 8

Either 8 or 1

Either 8 or 6

Solution

Question 2

3

9

7

4

Solution

Question 3

a + 2b + c is divisible by 3

2a + b + c is divisible by 3

a + b + 2c is divisible by 3

a + b + c is divisible by 3

Question 4

240

576

4800

4848

Solution

Question 5

All even natural numbers which are divisible by 3 are also divisible by 6.

If a natural number is divisible by 21, then it is divisible by both 3 and 7.

If AB × 4 = 192, then A + B = 10

A number of the form 14 N + 2 leaves the remainder 2 when divided by 7.

Question 6

1

3

0

infinite

Solution

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