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If f(5 + x) = f(5 - x) for every real x | Quantitative Aptitude - CAT Progression

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The question below is from previous year CAT question from CAT 2020 exam comes from CAT Progression: If f(5 + x) = f(5 – x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:

CAT 2020 - Slot 1 - Quantitative Aptitude - Question 2: If f(5 + x) = f(5 - x) for every real x

Q.2 : If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

1.  0
2. 40
3.  10
4.  20

Correct Answer: 20

Given f (5 + x) = f (5 – x)

When x = 1, f(6) = f(4)

When x = 2, f(7) = f(3)

Imagine a graph and while joining (6,4) and (7,3) it looks symmetrical about 5

Given 4 distinct real roots. Assume 12 as one of the roots.

f(12) = 0 –> Then f(5 + 7) = 0 which is same as f(5 – 7) = f(-2) = 0

So the roots are in the form (5 + k) and (5 – k) {This is one pair}

Sum of the roots = 5 + k + 5 – k = 10

We have 4 roots, So two pairs =10 + 10 = 20

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