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01. (1000)9 ÷ 1024 = ?
A. 10000 B. 1000
C. 100 D. 10
E. None of these

Answer and Explanation

Answer: 1000

Explanation:
(1000)9 / 1024   = (103)9 / 1024 = (10)27 / 1024


10(27-24) = 103 = 1000

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02. The difference between a two-digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
A. 3 B. 4
C. 9 D. Cannot be determined
E. None of these

Answer and Explanation

Answer: 4

Explanation:
Let the ten's digit be x and unit's digit be y.
Then, (10x + y) - (10y + x) = 36
9(x - y) = 36
x - y = 4

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03. In a two-digit, if it is known that its unit's digit exceeds its ten's digit by 2 and that the product of the given number and the sum of its digits is equal to 144, then the number is
A. 24 B. 26
C. 42 D. 46

Answer and Explanation

Answer: 24

Explanation:
Let the ten's digit be x.
Then, unit's digit = x + 2.
Number = 10x + (x + 2) = 11x + 2.
Sum of digits = x + (x + 2) = 2x + 2.
(11x + 2)(2x + 2) = 144
22x2 + 26x - 140 = 0
11x2 + 13x - 70 = 0
(x - 2)(11x + 35) = 0
x = 2.
Hence, required number = 11x + 2 = 24.

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04. The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is
A. 380 B. 395
C. 400 D. 425

Answer and Explanation

Answer: 400

Explanation:
Let the numbers be x and y.
Then, xy = 9375 and x = 15.
y
xy = 9375
(x/y) 15
y2 = 625.
y = 25.
x = 15y = (15 x 25) = 375.
Sum of the numbers = x + y = 375 + 25 = 400.

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05. A number consists of 3 digits whose sum is 10. The middle digit is equal to the sum of the other two and the number will be increased by 99 if its digits are reversed. The number is
A. 145 B. 253
C. 370 D. 352

Answer and Explanation

Answer: 253

Explanation:
Let the middle digit be x.
Then, 2x = 10 or x = 5. So, the number is either 253 or 352.
Since the number increases on reversing the digits, so the hundred's digits is smaller than the unit's digit.
Hence, required number = 253.

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06. If x, x+2 and x+4 are prime numbers, then find the number of possible solutions for x.
A. 1 B. 2
C. 3 D. 4

Answer and Explanation

Answer: 1

Explanation:
For x=2, the numbers are: 2, 4, 6 … (only first number is a prime number)
For x=3, the numbers are: 3, 5, 7 … (all numbers are prime numbers)
For x=5, the numbers are 5, 7, 9 … (first two numbers are prime numbers)
Hence for all other possibilities of x as a prime number, x, x+2 and x+4 all are not prime numbers.
Therefore there is only one possibility of x.

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07. 3/4th of a number exceeds its 2/3rd by 8. What is the number?
A. 96 B. 36
C. 72 D. 144

Answer and Explanation

Answer: 72

Explanation:
Let the number be x.
3/4x = 2/3x + 8
Multiply by 12
9x = 8x + 72
x = 72

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08. How many numbers between 100 and 600 are divisible by 2, 3, and 7 together?
A. 11 B. 12
C. 14 D. cannot be determined

Answer and Explanation

Answer: 12

Explanation:
As the division is by 2, 3, 7 together, the numbers are to be divisible by: 2*3*7 = 42
The limits are 100 and 600
The first number divisible is 42*3 = 126
To find out the last number divisible by 42 within 600:
600/42 = 14.28
Hence, 42*14 = 588 is the last number divisible by 42 within 600
Hence, total numbers divisible by 2, 3, 7 together are (14 – 2) = 12

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09. A positive integer which when added to 100, gives a sum which is greater than when it is multiplied by 100. What is the number
A. 5 B. 2
C. 3 D. 1

Answer and Explanation

Answer: 1

Explanation:
The number is 1

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10. Find the least value of x and y so that the number 5x423y is divisible by 88.
A. 8, 2 B. 9, 4
C. 7, 3 D. 8, 5

Answer and Explanation

Answer: 8, 2

Explanation:
As 88 is an even number, option (c) and (d) are eliminated. Substituting the values of (a) and (b) and solving the answer is (a)

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