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Which of the following is not a multiple of 3, 7 and 19? Indicate all such options.

7980

234901

9975

3591

185191

Correct Answer: B and E

Explanation:

7980=3*7*19*20
234901 is not divisible by 3
9975=3*7*19*25
3591=3*7*19*9
185191 is not divisible by 3
Hence, (B) and (E) are the correct options.

Question 2

Which of the following statements is true about the number 34983? Indicate all such options.

It is not a perfect square.

It is divisible by 13^{2}

It becomes a perfect square when it is divided by 23

It becomes a perfect square when it is multiplied by 23

It is divisible by 23^{2}

Correct Answer: A, B, C and D

Explanation:

34983=3*3*13*13*23
It is not a perfect square.
It is divisible by 13^{2}
It becomes a perfect square when it is either divided or multiplied by 23.
It is not divisible by 23^{2}
Hence, A, B, C and D are true.

Question 3

What are the remainders when 8^{6+6} is divided by 7 and 8? Indicate all correct options.

0

1

2

3

6

Correct Answer: A and E

Explanation:

8 divided by 7 leaves remainder 1
8^{2} divided by 7 leaves remainder 1
and so on...8^{6} divided by 7 leaves remainder 1.
8^{6+6} divided by 7 leaves remainder 1+6=7, which is again divisible by 7
Hence, remainder is 0.

8 divided by 8 leaves remainder 0
8^{2} divided by 8 leaves remainder 0
and so on...8^{6} divided by 8 leaves remainder 0.
8^{6+6} divided by 8 leaves remainder 0+6=6.
Hence, remainder is 6.
Options A and E are true.

Question 4

In a class of 20 girls and 40 boys, 20% of the girls are 12 years old and 40% of all the students are 12 years old. Which of the following statements is true? Indicate all such statements.

50% of the boys are 12 years old

5 girls are 12 years old

35 students in the class are 12 years old

20 boys are 12 years old

50% of the children who are 12 years old are boys

Correct Answer: A and D

Explanation:

Number of girls = 20
Number of boys = 40
Total students = 20+40=60
12 year old girls = 20% of 20 = 20*20/100 = 4
12 year old children = 40% of 60 = 40*60/100 = 24
12 year old boys = 24 - 4 = 20
Percentage of boys who are 12 years old = 20/40*100=50%
Percentage of 12 year old children who are boys = 20/24*100 = 83.33%
Option A is true.
Option B is false.
Option C is false.
Option D is true and E is false.

Question 5

The average of 10 numbers is 7. Which of the following statements is true? Indicate all true statements.

The average increases by 1 if each number increases by 1

The average becomes 3 times, if each number becomes three times

If the sum of the numbers increases by 7, the average increases by 1

If seven numbers increase by 3 each and three numbers decrease by 7 each, the average remains the same

The sum of the numbers is 70

Correct Answer: A, B, D and E

Explanation:

Average = 7 and number of observations = 10
Sum of observations = Average* number of observations
= 7*10=70
Option E is true.

If each number increases by 1, then the sum increases by 70+10=80
Average = 80/10=8
Average increases by 1
Option A is true.

If each number becomes three times, the sum also becomes three times.
Average = 3*70/10=3*7=21
Option B is true.

If the sum increases by 7, it becomes 70+7=77
Average = 77/10=7.7
Option C is false.

If 7 numbers increase by 3 and 3 decrease by 7, then sum = 70+7*3-3*7 = 70+21-21=70
Average = 70/10=7
Option D is true.

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