Numbers problems
- 1. 476 ** 0 is divisible by both 3 and 11.The non zero digits in the hundred's and ten's places are respectively:
Options- A. 6 and 2
- B. 8 and 2
- C. 6 and 5
- D. 8 and 5 Discuss
Correct Answer: 8 and 5
Explanation:
Let the number be 476ab0
476ab0 is divisible by 3
=> 4 + 7 + 6 + a + b + 0 is divisible by 3
=> 17 + a + b is divisible by 3 ------------------------(i)
476ab0 is divisible by 11
[(4 + 6 + b) -(7 + a + 0)] is 0 or divisible by 11
=> [3 + (b - a)] is 0 or divisible by 11 --------------(ii)
Substitute the values of a and b with the values given in the choices and select the values which satisfies both Equation 1 and Equation 2.
if a=6 and b=2,
17 + a + b = 17 + 6 + 2 = 25 which is not divisible by 3 --- Does not meet equation(i).Hence this is not the answer
if a=8 and b=2,
17 + a + b = 17 + 8 + 2 = 27 which is divisible by 3 --- Meet equation(i)
[3 + (b - a)] = [3 + (2 - 8)] = -3 which is neither 0 nor divisible by 11---Does not meet equation(ii).Hence this is not the answer
if a=6 and b=5,
17 + a + b = 17 + 6 + 5 = 28 which is not divisible by 3 --- Does not meet equation (i) .Hence this is not the answer
if a=8 and b=5,
17 + a + b = 17 + 8 + 5 = 30 which is divisible by 3 --- Meet equation 1
[3 + (b - a)] = [3 + (5 - 8)] = 0 ---Meet equation 2
Since these values satisfies both equation 1 and equation 2, this is the answer
- 2. Find the next number in the series 14, 916, 2536,......
Options- A. 4981
- B. 6481
- C. 4964
- D. 6449 Also asked in: CAT, Bank Exams, Bank PO, Bank Clerk
Correct Answer: 4964
Explanation:
The pattern is ,
The next number= = 4964
- 3. 7, 16, 36, 78, 144, ? which number come in place of question mark
Options- A. 168
- B. 196
- C. 222
- D. 256 Also asked in: Bank Exams, Bank PO
Correct Answer: 222
- 4. Which one of the following cannot be the square of a natural number?
Options- A. 32761
- B. 42437
- C. 81225
- D. 20164 Discuss
Correct Answer: 42437
Explanation:
The square of a natural number never ends in 7.
42437 is not the square of a natural number
- 5. The largest 4 digit number exactly divisible by 88 is ?
Options- A. 9944
- B. 9768
- C. 8888
- D. 9988 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk
Correct Answer: 9944
Explanation:
The largest 4 digit number is = 9999
After dividing 9999 with 88, we get 55 as remainder
so largest 4 digit number divisible by 88 = 9999-55 = 9944.
- 6. How many numbers up to 300 and 700 are divisible by 2, 3 and 7 both together ?
Options- A. 7
- B. 9
- C. 11
- D. 5 Also asked in: AIEEE, Bank Exams, CAT, Bank Clerk, Bank PO
Correct Answer: 9
Explanation:
LCM of 2, 3, 7 is 42.
=> (700 ? 300)/42 = 9 22/42 => 9 Numbers.
- 7. The sum of the two numbers is 12 and their product is 35.What is the sum of the reciprocals of these numbers?
Options- A. 12/35
- B. 1/35
- C. 35/8
- D. 7/32 Discuss
Correct Answer: 12/35
Explanation:
Let a and b are the numbers.Then a+b is 12 and ab is 35.
a+b/ab = 12/35
1/b + 1/a = 12/35
- 8. What smallest number should be added to 4456 so that the sum is completely divisible by 6 ?
Options- A. 4
- B. 3
- C. 2
- D. 1 Discuss
Correct Answer: 2
Explanation:
6)4456(742
42
--------
25
24
-------
16
12
-----
4
------
Required number = (6-4) = 2.
- 9. How many of the following numbers are divisible by 132? 264,396,462,792,968,2178,5184,6336
Options- A. 4
- B. 5
- C. 6
- D. 7 Discuss
Correct Answer: 4
Explanation:
132 = 4 x 3 x 11, So if the number is divisible by all three numbers 4,3 and 11,then the number is divisible by 132 also.
264 => 4,3,11(/)
396 => 4,3,11(/)
462 => 11,3
792 => 4,3,11(/)
968 => 11,4
2178 => 11,3
5184 => 3,4
6336 => 4,3,11(/)
Required number of numbers=4.
- 10. If the number 517?324 is completely divisible by 3,then the smallest whole number in place of ? will be:
Options- A. 2
- B. 1
- C. 3
- D. 7 Discuss
Correct Answer: 2
Explanation:
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = ( 22 + x ), which must be divisible by 3.
When x=2. [(22 + 2) = 24 is divisible by 3]
So, the answer is 2
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