Number System - Study Mode

[#326] A two-digit number, 9A, is a prime number. Find A.
Correct Answer

(B) 7

Explanation

Solution: 9A is prime number then by option, 9A Option A: A = 9, Number = 99 → Composite Option B: A = 7, Number = 97 → Prime Option C: A = 3, Number = 93 → Composite Option D: A = 1, Number = 91 → Composite

[#327] What is the value of x so that the seven digit number 8439x53 is divisible by 99?
Correct Answer

(B) 4

Explanation

Solution: 8 + 4 + 3 + 9 + x + 5 + 3 = 9 or multiple of x + 5 = 9 x = 4

[#328] The sum of the digits of a two digit number is $$frac{1}{7}$$ of the number. The units digit is 4 less than the tens digit. If the number obtained on reversing its digits is divided by 7, the remainder will be:
Correct Answer

(B) 6

Explanation

Solution: $$eqalign{
& x + y = frac{1}{7}left( {10x + y}
ight) cr
& 7x + 7y = 10x + y cr
& 3x = 6y cr
& x:y = 2:1 cr
& 1{ ext{ unit}} o { ext{4}} cr
& { ext{Number will be}} = 84 cr
& frac{{48}}{7}R o 6 cr} $$

[#329] Two positive whole numbers are such that the sum of the first and twice the second number is 8 and their difference is 2. The numbers are:
Correct Answer

(D) 4, 2

Explanation

Solution: In such type of question always go through option to save your valuable time. By option D: 4, 2 4 + 2 × 2 = 8 4 - 2 = 2 (Satisfied)

[#330] A and B are positive integers. If A + B + AB = 65, then what is the
difference between A and B (A, B ≤ 15)?
Correct Answer

(C) 5

Explanation

Solution: A + B + AB = 65 (A, B ≤ 15) Assume value of A & B A = 10 B = 5 10 + 5 + 10 × 5 = 65 65 = 65 value satisfied Difference between (A - B) = 10 - 5 = 5