Number System problems
- 1. When simplified, the product ( 2 - 1/3) (2 - 3/5) (2 - 5/7) ...... (2 - 997/999) is equal to?
Options- A. 5/999
- B. 1001/999
- C. 1001/3
- D. None of these Discuss
Correct Answer: 1001/3
Explanation:
Given Exp. ( 2 - 1/3) (2 - 3/5) (2 - 5/7) ...... (2 - 997/999)
= (5/3) x (7/5) x (9/7) x .......... x (1001/999)
= 1001/3.
- 2. (1 - 1/3) (1 - 1/4) (1 - 1/5 )... (1 - 1/n ) =?
Options- A. 1/n
- B. 2/n
- C. 2(n - 1)/n
- D. 2(n + 1)/n Discuss
Correct Answer: 2/n
Explanation:
Given Exp.= (1 - 1/3) (1 - 1/4) (1 - 1/5)...(1 - 1/n)
= (2/3) x (3/4) x (4/5) x ... x (n-1/n)
= 2/n.
- 3. Which of the following numbers is exactly divisible by 99?
Options- A. 3572404
- B. 135792
- C. 913464
- D. 114345 Discuss
Correct Answer: 114345
Explanation:
To determine if a number is divisible by 99 it needs to be divisible by 9 and 11.
Divisible by 9 test. If sum of digits is divisible by 9 then the number is divisible by 9.
Divisible by 11 test. If sum of ODD positioned digits minus the sum of the EVEN positioned digits is divisible by 11 then the number is divisible by 11.
Clearly 114345 is divisible by 9 as well as 11. so,it is divisible by 99.
- 4. What least value must be given to * so that the number 91876 * 2 is divisible by 8?
Options- A. 1
- B. 2
- C. 3
- D. 4 Also asked in: Bank Exams
Correct Answer: 3
Explanation:
By hit and trial we find that 632 is divisible by 8. So, * must replaced by 3.
- 5. What least value must be given to * so that the number 6135 * 2 is exactly divisible by 9?
Options- A. 0
- B. 1
- C. 2
- D. 3 Discuss
Correct Answer: 1
Explanation:
6 + 1 + 3 + 5 + x + 2 = 17 + x must be divisible by 9.
So, x =1.
- 6. What least value must be given to * so that the number 97215*6 is divisible by 11?
Options- A. 1
- B. 2
- C. 3
- D. 5 Discuss
Correct Answer: 3
Explanation:
If sum of ODD positioned digits minus the sum of the EVEN positioned digits is divisible by 11 then the number is divisible by 11.
Sum of odd positioned digits - sum of even positioned digits = (9 + 2 + 5 + 6) - (7 + 1 + x) =14 - x
It must be divisible by 11. So x = 3.
- 7. What least number must be added to 1056 get a number exactly divisible by 23?
Options- A. 21
- B. 25
- C. 3
- D. 2 Discuss
Correct Answer: 2
Explanation:
On dividing 1056 by 23, we get 21 as remainder
? Required number to be added = (23 - 21 ) = 2.
- 8. The number (10 n-1) is divisible by 11 for?
Options- A. All Values of n
- B. Odd values of n
- C. Even values of n
- D. n = multiples of 11 Discuss
Correct Answer: Even values of n
Explanation:
For even values of n, the number (10n - 1 ) consists of even numbers of nines and hence it will be divisible by 11.
- 9. Which of the following numbers is prime?
Options- A. 119
- B. 187
- C. 247
- D. None of these Discuss
Correct Answer: None of these
Explanation:
119 is divisible by 7, 187 is divisible by 11,247 is divisible by 13 and 551 is divisible by 19. So none of the given numbers is prime.
- 10. If in a long division sum,the dividend is 380606 and the successive remainders from the first to the last are 434, 125 and 413, then the divisor is?
Options- A. 451
- B. 843
- C. 4215
- D. 3372 Discuss
Correct Answer: 843
Explanation:
Let d = divisor and q = quotient
First remove the last remainder:
d x q + 413 = 380606
d x q = 380193
So d cannot be even (choice d) or a multiple of 5 (choice c).
If we try choice a or b,
a quick division (by calculator) shows that
380193 = 451 x 843, the other two choices.
(In the absence of choices, we could find the prime factors of 380193,
which are 3 x 11 x 41 x 281 and get various candidate divisors from that.)
So one of them is the divisor and the other the quotient.
So we can just check the first remainder:
843 x 4 = 3372
3806 - 3372 = 434 ... a match!
And just to be sure:
451 x 8 = 3608
3806 - 3608 = 198
So the divisor is 843.
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