number system Model Questions & Answers, Practice Test for ssc steno grade c d 2024

Answer: (d)

All the given statements are true.

The following are the examples for all the statements

Statement 1:

Both p and q may be prime numbers.

Ex – 7 and 11

Statement 2:

Both p and q may be composite numbers.

Ex – 8 and 12

Statement 3:

One of p and q may be prime and the other composite.

Ex. 13 and 16

Answer: (d)

For prime no units place cannot be occupied by even number except for 2

Thus no of digits occupying unit digit of prime numbers = 6 (1, 2, 3, 5, 7, 9)

Answer: (b)

If we look at the numbers 100 < N ≤ 105, we see only 101 and 103 do not have their factors in N (because these are primes).

So, obviously the new LCM will be 101 × 103 × N.

Answer: (c)

Sum of all even factors:

$(2^1) (5^0 + 5^1 + 5^2) (7^0 + 7^1 + 7^2)$ = 3534

Number of even factors = 1 × 3 × 3 = 9

Answer: (c)

The given fractions are $1/2 , 2/3 , 5/9 , 6/13$ and $7/9$

LCM of their denominators is 234

∴ ${117,78, 26,18, 26}/234$

${117, 2 × 78,5 × 26,6 × 18,7 × 26}/234$

${117,156,130,108,182}/234$

On arranging the numerators in ascending order 108, 117, 130, 156, 182.

∴ Ascending order of the fraction is

$6/13 < 1/2 < 5/9 < 2/3 < 7/9$