number system Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

Answer: (d)

The unit digit of every term from 5! to 49! is 0.

Also, 1! – 2! + 3! – 4! = 1 – 2 + 6 – 24 = –19.

Hence, the unit digit of N will be 10 – 9 = 1.

The unit digit of $N^N$ will also be 1.

Answer: (c)

Let greater number = x

smaller number = y

∴ x + y = 90 ...(1)

and x – 3y = 14 ...(2)

By equation (1) + (2)

x = 71, y = 19

∴ smaller number = 19

greater number = 71

Answer: (d)

$3y^2 = x^2 – 1376$

As we can see L.H.S. is definitely a multiple of 3 and in R.H.S. 1376 leaves a remainder of 2 when divided by 3.

There are three possibilities for x in R.H.S:

1. If x is multiple of 3, so is $x^2$ , and R.H.S. will leave a remainder of 1 when divided by 3.
2. If x is of the form 3m + 1, $x^2$ will be of the form 3n + 1 and R.H.S will leave a remainder of 2. m, n∈ N
3. If x is of the form 3m + 2, $x^2$ will be of the form 3n + 1 and R.H.S. will leave a remainder of 2. m, n∈ N So R.H.S. can never be a multiple of 3, while L.H.S. is always a multiple of 3. Hence no real solution exists.

Answer: (d)

On taking option (d).

The reverse digit of 451 is 154.

Now, 154 + 297 = 451 is equal to the original number.

Answer: (b)

The total number of thee digit numbers with unit digit 7 and divisible by 11 are 187, 297, 407, 517, 627, 737, 847, 957.

∴ Total numbers = 8