Numbers problems
- 1. A number when divided by 296 leaves 75 as remainder.When the same number is divided by 37,the remainder will be:
Options- A. 1
- B. 3
- C. 5
- D. 2 Discuss
Correct Answer: 1
Explanation:
Let the Number be Y.
Then Y = 296 q + 75
= (37 x 8)q +( 37 x 2) + 1
= 37 (8q + 2) + 1
Thus, when the number is divided by 37, the remainder is 1
- 2. On dividing 2272 as well as 875 by 3-digit number N,we get the same remainder.The sum of the digits of N is:
Options- A. 13
- B. 12
- C. 11
- D. 10 Discuss
Correct Answer: 10
Explanation:
(2272-875) = 1397, is exactly divisible by N.
Now , 1397 = 11 x 127
The required 3-digit number is 127,the sum of digits is 10.
- 3. If the product 4864*9 P 2 is divisible by 12, the value of p:
Options- A. 1
- B. 2
- C. 3
- D. 4 Discuss
Correct Answer: 1
Explanation:
Clearly 4864 is divisible by 4
So, 9 P 2 must be divisible by 3. So (9+P+2) must be divisible by 3.
So P=1.
- 4. A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 98 are wrong and the other digits are correct , then the correct answer would be :
Options- A. 553681
- B. 555181
- C. 555681
- D. 556581 Discuss
Correct Answer: 555681
Explanation:
987 = 3 * 7 * 47.
So, the required number must be divisible by each one of 3, 7, 47
553681 => (Sum of digits = 28, not divisible by 3)
555181 => (Sum of digits = 25, not divisible by 3)
555681 is divisible by each one of 3, 7, 47.
- 5. The difference between the squares of two consecutive odd integers is always divisible by ?
Options- A. 8
- B. 2
- C. 6
- D. 4 Also asked in: CAT, Bank Clerk
Correct Answer: 8
Explanation:
Let the two consecutive odd integers be (2x + 1) and (2x + 3)
Then,
(2x + 3)2 - (2x + 1)2
= (2x + 3 + 2x + 1) (2x + 3 - 2x - 1)
= (4x + 4)(2)
= 8 (x + 1), which is always divisible by 8
- 6. On dividing 4150 by a certain number , the quotient is 55 and the remainder is 25, the divisor is
Options- A. 68
- B. 65
- C. 70
- D. 75 Discuss
Correct Answer: 75
Explanation:
Let Divisor be x. We know that Dividend = Remainder+Divisor×Quotient So Divisor = (Dividend - Remainder)/Quotient ⇒ x = (4150 - 25)/55 ⇒ x = 4125/55 ⇒ x = 75 Hence Divisor is 75.
- 7. Find the next number in the series 125, 80, 45, 20, ....
Options- A. 5
- B. 15
- C. -5
- D. 10 Also asked in: Bank Exams, CAT, Bank Clerk
Correct Answer: 5
Explanation:
The pattern is -45, -35, -25, -15
The next number = 20-15= 5
- 8. The difference between a positive proper fraction and its reciprocal is 9 / 20. Then the fraction is :
Options- A. 3/5
- B. 3/10
- C. 4/5
- D. 5/4 Discuss
Correct Answer: 4/5
Explanation:
Let the required fraction be x. Then, (1 / x )- x = 9/20
1 - x^(2) / x = 9 / 20 => 20 - 20 * x^(2) = 9 * x.
20 * x^(2) + 9 *x - 20 = 0.
=> (4 * x + 5) (5 * x - 4) = 0.
=> x = 4 / 5.
- 9. What is the greatest of 3 consecutive integers whose sum is 24 ?
Options- A. 6
- B. 7
- C. 8
- D. 9 Also asked in: GRE
Correct Answer: 9
Explanation:
The sum of three consecutive integers can be written as n + (n + 1) + (n + 2) = 3n + 3
If the sum is 24, we need to solve the equation 3n + 3 = 24;
=> 3n = 21;
=> n = 7
The greatest of the three numbers is therefore 7 + 2 = 9
- 10. If 60% of 35 of a number is 36, then the number is
Options- A. 86
- B. 94
- C. 100
- D. 115 Discuss
Correct Answer: 100
Explanation:
Let the number be x.Then
60% of of x=36.
=>
=> => x=
Required number is 100.
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