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The sum of two numbers is 156 and their HCF is 13. The numbers of such number pairs is
  • a)
    2
  • b)
    5
  • c)
    4
  • d)
    3
  • e)
    6
Correct answer is option 'A'. Can you explain this answer?
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The sum of two numbers is 156 and their HCF is 13. The numbers of such...
Highest Common Factor (HCF) is 13, that means
the numbers are multiples of 13.
We need sum of numbers to be 156.
In such sums, first write multiples of 13 till 156 
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Most Upvoted Answer
The sum of two numbers is 156 and their HCF is 13. The numbers of such...
Given:
Sum of two numbers = 156
HCF of two numbers = 13

To find:
Number of such number pairs

Solution:
Let the two numbers be 13a and 13b (as 13 is the HCF, we can take a and b as co-prime numbers)

We know that the sum of two numbers is 156

Therefore, 13a + 13b = 156

Dividing both sides by 13, we get:

a + b = 12

We need to find the number of pairs (a, b) that satisfy the above equation.

We can find these pairs by trial and error or by using a systematic approach:

- If a = 1, b = 11
- If a = 2, b = 10
- If a = 3, b = 9
- If a = 4, b = 8
- If a = 5, b = 7
- If a = 6, b = 6

So, there are only 2 pairs (a, b) that satisfy the equation a + b = 12 (i.e., (1, 11) and (2, 10))

Therefore, the answer is option A) 2.
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Directions: Read the given passage carefully and answer the question as follow.Among the speculative questions which arise in connection with the study of arithmetic from a historical standpoint, the origin of number is one that has provoked much lively discussion, and has led to a great amount of learned research among the primitive and savage languages of the human race. A few simple considerations will, however, show that such research must necessarily leave this question entirely unsettled, and will indicate clearly that it is, from the very nature of things, a question to which no definite and final answer can be given. Among the barbarous tribes whose languages have been studied, even in a most cursory manner, none have ever been discovered which did not show some familiarity with the number concept. The knowledge thus indicated has often proved to be most limited; not extending beyond the numbers 1 and 2, or 1, 2, and 3. At first thought it seems quite inconceivable that any human being should be destitute of the power of counting beyond 2. But such is the case; and in a few instances languages have been found to be absolutely destitute of pure numeral words.These facts must of necessity deter the mathematician from seeking to push his investigation too far back toward the very origin of number. Philosophers have endeavoured to establish certain propositions concerning this subject, but, as might have been expected, have failed to reach any common ground of agreement. Whewell has maintained that “such propositions as that two and three make five are necessary truths, containing in them an element of certainty beyond that which mere experience can give.” Mill, on the other hand, argues that any such statement merely expresses a truth derived from early and constant experience; and in this view he is heartily supported by Tylor.But why this question should provoke controversy, it is difficult for the mathematician to understand. Either view would seem to be correct, according to the standpoint from which the question is approached. We know of no language in which the suggestion of number does not appear, and we must admit that the words which give expression to the number sense would be among the early words to be formed in any language. They express ideas which are, at first, wholly concrete, which are of the greatest possible simplicity, and which seem in many ways to be clearly understood, even by the higher orders of the brute creation. The origin of number would in itself, then, appear to lie beyond the proper limits of inquiry; and the primitive conception of number to be fundamental with human thought.Q.The author of the passage would most probably agree with each of the following EXCEPT

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The sum of two numbers is 156 and their HCF is 13. The numbers of such number pairs isa)2b)5c)4d)3e)6Correct answer is option 'A'. Can you explain this answer?
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