PYQ Vault
EbooksTutor

Fraction expanded as a continued fraction to find the unknown integers

This type of question, asked 4 times: CDS 1 2019, CDS 2 2019, CDS 1 2022, CDS 1 2024. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 1 2019

    82
    If 3611=3+1x+1y+1z\frac{36}{11} = 3 + \cfrac{1}{x + \cfrac{1}{y + \cfrac{1}{z}}}, where xx, yy and zz are natural numbers, then what is (x+y+z)(x + y + z) equal to ?

    Tap an option to check your answer.

  2. Question 2

    CDS 2 2019

    15
    If a, b and c are positive integers such that 1a+1b+1c+12=1623\cfrac{1}{a + \cfrac{1}{b + \cfrac{1}{c + \cfrac{1}{2}}}} = \frac{16}{23}, then what is the mean of a, b and c ?

    Tap an option to check your answer.

  3. Question 3

    CDS 1 2022

    14
    Let aa, bb, cc, dd be positive integers. If 1a+1b+1c+1d=1760\cfrac{1}{a + \cfrac{1}{b + \cfrac{1}{c + \cfrac{1}{d}}}} = \frac{17}{60} then what is the product of aa, bb, cc, dd ?

    Tap an option to check your answer.

  4. Question 4

    CDS 1 2024

    36
    If 1a+1b+1c+1d+1e=421972\cfrac{1}{a + \cfrac{1}{b + \cfrac{1}{c + \cfrac{1}{d + \cfrac{1}{e}}}}} = \frac{421}{972}, then what is the value of a×b×c×d×ea \times b \times c \times d \times e ?

    Tap an option to check your answer.