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Quantitative Aptitude > Number System

RELATIONSHIPS BETWEEN NUMBERS MCQs

Total Questions : 3447 | Page 5 of 345 pages
Question 41.

\(\frac{392}{\sqrt{x}}\)  = 28  find the value of   x .   

  1.    156
  2.    184
  3.    196
  4.    124
 Discuss Question
Answer: Option C. -> 196
Question 42.

\(\sqrt{1 +\frac{27}{169}}\)    = 1 + \(\frac{x}{13}\) find the value of   x .

  1.    1
  2.    2
  3.    3
  4.    4
 Discuss Question
Answer: Option A. -> 1
Question 43.

For  odd no. of  n , the number 14 n  + 1 is divisible by

  1.    15
  2.    15
  3.    2
  4.    18
 Discuss Question
Answer: Option B. -> 15
Question 44.

Check 114345  is divisible by :

  1.    19
  2.    39
  3.    53
  4.    99
 Discuss Question
Answer: Option D. -> 99
Question 45.

  1. Solve y :  \(\frac{y - 1}{y}\)  >  0

  1.    y=0
  2.    y=1
  3.    y<0
  4.    y>0
 Discuss Question
Answer: Option C. -> y<0
Question 46.

  1. Find the unit’s digit in the product  274 x 318 x 577 x 313 .

  1.    1
  2.    3
  3.    3
  4.    4
 Discuss Question
Answer: Option B. -> 3
Question 47.

  1. Find the unit place  of  ( 3127 ) 173 .

  1.    3
  2.    5
  3.    7
  4.    9
 Discuss Question
Answer: Option C. -> 7
Question 48.

A six – digit no. is framed by repeating a three digitnu. For example 256256 or 678678 any numbers of this form is always exactly divisible by.

  1.    7 only
  2.    11 only
  3.    13 only
  4.    1001 only
 Discuss Question
Answer: Option D. -> 1001 only
Question 49.

  1. The least number which  must be subtracted from 6709 to make it exactly divisible by9 .

  1.    2
  2.    3
  3.    4
  4.    5
 Discuss Question
Answer: Option C. -> 4
Question 50.

When the sum two no. is multiplied by 5 the product divisible by 15 . Check ( 245 + 342) pairs of numbers satisfies the above condition  ?

  1.    240,335
  2.    250,341
  3.    245,342
  4.    none of these
 Discuss Question
Answer: Option B. -> 250,341
To check if the sum of two numbers is divisible by 3 and 5, we need to apply the following conditions:
Condition 1: The sum of the two numbers must be divisible by 3.Condition 2: The product of the sum of the two numbers and 5 must be divisible by 3.
Let's apply these conditions to the given pairs of numbers (245 + 342) to see if they satisfy the condition.
Condition 1: To check if the sum of two numbers is divisible by 3, we need to find the sum of the digits of the numbers and see if the sum is divisible by 3.
Sum of digits of 245 = 2 + 4 + 5 = 11Sum of digits of 342 = 3 + 4 + 2 = 9
So, the sum of the digits of both numbers is not divisible by 3. Hence, the sum of the two numbers is not divisible by 3.Therefore, we can conclude that none of the given pairs of numbers (240, 335), (250, 341), and (245, 342) satisfy the condition that the sum of two numbers is divisible by 3.
Condition 2: To check if the product of the sum of two numbers and 5 is divisible by 3, we need to check if the sum of the two numbers is divisible by 3.
As we have already seen that the sum of the two numbers is not divisible by 3, we do not need to check this condition.
However, we still need to check if the product of the sum of two numbers and 5 is divisible by 15.
Product of (245 + 342) = 587 * 5 = 2935
2935 is divisible by 15, as 15 * 195 = 2935
Hence, the given pair of numbers (245, 342) satisfies the condition that the product of the sum of two numbers and 5 is divisible by 15.
Therefore, the correct answer is option B (250, 341).
Formulae:
  • Divisibility rule for 3: If the sum of the digits of a number is divisible by 3, then the number is also divisible by 3.
  • Divisibility rule for 15: If a number is divisible by both 3 and 5, then it is also divisible by 15.
Key Points:
  • To check if the sum of two numbers is divisible by 3, we need to find the sum of the digits of the numbers and see if the sum is divisible by 3.
  • To check if the product of the sum of two numbers and 5 is divisible by 15, we need to check if the sum of the two numbers is divisible by both 3 and 5.
  • The given pair of numbers (245, 342) satisfies the condition that the product of the sum of two numbers and 5 is divisible by 15.
If you think the solution is wrong then please provide your own solution below in the comments section .

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