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Two numbers written as h x a and h x b with a, b coprime, from their HCF and product, LCM or ratio

This type of question, asked 6 times: CDS 1 2018, CDS 2 2018, CDS 1 2020, CDS 1 2022, CDS 1 2023, CDS 2 2026. All 6 questions below, oldest first.

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  1. Question 1

    CDS 1 2018

    14
    There are two numbers which are greater than 21 and their LCM and HCF are 3003 and 21 respectively. What is the sum of these numbers?

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  2. Question 2

    CDS 2 2018

    13
    The product of two integers p and q, where p > 60 and q > 60, is 7168 and their HCF is 16. The sum of these two integers is

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  3. Question 3

    CDS 1 2020

    2
    Two unequal pairs of numbers satisfy the following conditions : (i) The product of the two numbers in each pair is 2160 (ii) The HCF of the two numbers in each pair is 12. If xx is the mean of the numbers in the first pair and yy is the mean of the numbers in the second pair, then what is the mean of xx and yy ?

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  4. Question 4

    CDS 1 2022

    5
    Suppose pp and qq are the LCM and HCF respectively of two positive numbers. If p:q=14:1p : q = 14 : 1 and pq=1134pq = 1134, then what is the difference between the two numbers?

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  5. Question 5

    CDS 1 2023

    27
    The product of two numbers is 2160 and their HCF is 12. If the sum of the squares of the two numbers is 4896, then what is the mean of the two numbers?

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  6. Question 6

    CDS 2 2026

    1
    Two positive integers x and y are in the ratio 17 : 19. If the LCM of the two numbers is 1615, then what is x+yx + y equal to ?

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