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Quantitative Aptitude > Number System

RELATIONSHIPS BETWEEN NUMBERS MCQs

Total Questions : 3447 | Page 6 of 345 pages
Question 51.

A no. when divided by the sum of 555 and 445 gives two times their difference as quotient and 30 as the remainder

  1.    1220
  2.    1250
  3.    22030
  4.    220030
 Discuss Question
Answer: Option D. -> 220030
Question 52.

A  no. divided by 899 gives a remainders 63 if the same no. is divided by 29.  Find  the remainder.

  1.    3
  2.    4
  3.    5
  4.    6
 Discuss Question
Answer: Option C. -> 5
Question 53.

How many no.Between 200 and 600 are divisible by 4, 5, and 6 ?

  1.    2
  2.    4
  3.    6
  4.    8
 Discuss Question
Answer: Option C. -> 6
Question 54.

Which one of the following is not a prime number?

  1.    31
  2.    61
  3.    71
  4.    91
 Discuss Question
Answer: Option D. -> 91

91 is divisible by 7. So, it is not a prime number.

Question 55.

\(\left(112\times5^{4}\right) = ?\)

  1.    67000
  2.    70000
  3.    76500
  4.    77200
 Discuss Question
Answer: Option B. -> 70000

\(\left(112\times5^{4}\right) = 112\times\left(\frac{10}{2}\right)^{4}=\frac{112\times10^{4}}{2^{4}}=\frac{1120000}{16}=70000\)

Question 56.

It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

  1.    (216 + 1)
  2.    (216 - 1)
  3.    (7 x 223)
  4.    (296 + 1)
 Discuss Question
Answer: Option D. -> (296 + 1)

Let 232 = x. Then, (232 + 1) = (x + 1).


Let (x + 1) be completely divisible by the natural number N. Then,


(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely


divisible by N, since (x + 1) is divisible by N.

Question 57.

What least number must be added to 1056, so that the sum is completely divisible by 23 ?

  1.    2
  2.    3
  3.    18
  4.    21
  5.    None of these
 Discuss Question
Answer: Option A. -> 2

23) 1056 (45


      92


      ---


      136


      115


      ---


       21


      ---


Required number = (23 - 21)   


                 = 2.  

Question 58.

1397 x 1397 = ?

  1.    1951609
  2.    1981709
  3.    18362619
  4.    2031719
 Discuss Question
Answer: Option A. -> 1951609

1397 x 1397 = (1397)2


= (1400 - 3)


= (1400)2 + (3)2 - (2 x 1400 x 3)


= 1960000 + 9 - 8400


= 1960009 - 8400


= 1951609.

Question 59.

How many of the following numbers are divisible by 132 ?
264, 396, 462, 792, 968, 2178, 5184, 6336

  1.    4
  2.    5
  3.    6
  4.    7
 Discuss Question
Answer: Option A. -> 4

132 = 4 x 3 x 11


So, if the number divisible by all the three number 4, 3 and 11, then the number is divisible by 132 also.


264\(\rightarrow\)  11,3,4 (/)


396\(\rightarrow\)  11,3,4 (/)


462  \(\rightarrow\)11,3 (X)


792 \(\rightarrow\) 11,3,4 (/)


968\(\rightarrow\)  11,4 (X)


2178 \(\rightarrow\) 11,3 (X)


5184\(\rightarrow\)  3,4 (X)


6336 \(\rightarrow\) 11,3,4 (/)


Therefore the following numbers are divisible by 132 : 264, 396, 792 and 6336.


Required number of number = 4.

Divisibility Rules:
A number is divisible by 2 if its last digit is 0, 2, 4, 6 or 8.
A number is divisible by 3 if the sum of its digits is divisible by 3.
A number is divisible by 4 if the number formed by its last two digits is divisible by 4.
A number is divisible by 5 if its last digit is 0 or 5.
A number is divisible by 6 if it is divisible by 2 and 3.
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
A number is divisible by 9 if the sum of its digits is divisible by 9.
A number is divisible by 10 if its last digit is 0.
A number is divisible by 11 if the difference between the sum of its digits in the odd places and the sum of its digits in the even places is either 0 or a multiple of 11.
A number is divisible by 12 if it is divisible by 3 and 4.
A number is divisible by 14 if it is divisible by 2 and 7.
A number is divisible by 15 if it is divisible by 3 and 5.
A number is divisible by 18 if it is divisible by 2, 3 and 6.

Divisibility by 132:
A number is divisible by 132 if it is divisible by 3 and 11 and 4.

Now, let us check whether given numbers are divisible by 132 or not:
264: The number 264 is divisible by 3 as the sum of its digits (2 + 6 + 4) = 12 is divisible by 3. It is also divisible by 4 as the last two digits (64) are divisible by 4. Also, it is divisible by 11 as 11 divides the difference between the sum of its digits in the odd places (2 + 4) = 6 and the sum of its digits in the even places (6) = 6. Therefore, 264 is divisible by 132.
396: The number 396 is divisible by 3 as the sum of its digits (3 + 9 + 6) = 18 is divisible by 3. It is also divisible by 4 as the last two digits (96) are divisible by 4. Also, it is divisible by 11 as 11 divides the difference between the sum of its digits in the odd places (3 + 6) = 9 and the sum of its digits in the even places (9) = 9. Therefore, 396 is divisible by 132.
462: The number 462 is not divisible by 3 as the sum of its digits (4 + 6 + 2) = 12 is not divisible by 3. Therefore, 462 is not divisible by 132.
792: The number 792 is divisible by 3 as the sum of its digits (7 + 9 + 2) = 18 is divisible by 3. It is also divisible by 4 as the last two digits (92) are divisible by 4. Also, it is divisible by 11 as 11 divides the difference between the sum of its digits in the odd places (7 + 2) = 9 and the sum of its digits in the even places (9) = 9. Therefore, 792 is divisible by 132.
968: The number 968 is divisible by 3 as the sum of its digits (9 + 6 + 8) = 23 is divisible by 3. It is also divisible by 4 as the last two digits (68) are divisible by 4. Also, it is divisible by 11 as 11 divides the difference between the sum of its digits in the odd places (9 + 8) = 17 and the sum of its digits in the even places (6) = 6. Therefore, 968 is divisible by 132.
2178: The number 2178 is not divisible by 3 as the sum of its digits (2 + 1 + 7 + 8) = 18 is not divisible by 3. Therefore, 2178 is not divisible by 132.
5184: The number 5184 is divisible by 3 as the sum of its digits (5 + 1 + 8 + 4) = 18 is divisible by 3. It is also divisible by 4 as the last two digits (84) are divisible by 4. Also, it is divisible by 11 as 11 divides the difference between the sum of its digits in the odd places (5 + 8) = 13 and the sum of its digits in the even places (1 + 4) = 5. Therefore, 5184 is divisible by 132.
6336: The number 6336 is divisible by 3 as the sum of its digits (6 + 3 + 3 + 6) = 18 is divisible by 3. It is also divisible by 4 as the last two digits (36) are divisible by 4. Also, it is divisible by 11 as 11 divides the difference between the sum of its digits in the odd places (6 + 6) = 12 and the sum of its digits in the even places (3 + 3) = 6. Therefore, 6336 is divisible by 132.

Hence, out of the given eight numbers, four numbers (264, 396, 792, 5184) are divisible by 132. Therefore, the correct answer is Option A. 4.

If you think the solution is wrong then please provide your own solution below in the comments section .

Question 60.

(935421 x 625) = ?

  1.    575648125
  2.    584638125
  3.    584649125
  4.    585628125
 Discuss Question
Answer: Option B. -> 584638125

935421 x 625 = 935421 x 54 = 935421 x \(\left(\frac{10}{2}\right)^{4}\)


= \(=\frac{935421\times10^{4}}{2^{4}} = \frac{9354210000}{16}\)


= 584638125

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