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Q36·CSAT · Prelims 2025

Ratio of max (x+y) to min (x-y)

NumericalInequalities & RangesAlgebra & equationsMedium

Question

If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7 then what is the ratio of maximum value of (x + y) to minimum value of (x - y)?

Options

a

6

b

15/2

c

-15/2

d

None of the above

Answer

Explanation

To maximize (x+y), we take the maximum possible values for both variables: \max(x) + \max(y) = 8 + 7 = 15. To minimize (x-y), we must start with the smallest possible value for x and subtract the largest possible value for y: \min(x) - \max(y) = 4 - 7 = -3. The required ratio is the maximum value divided by the minimum value. Ratio = 15 / -3 = -5. Since -5 is not among the given numerical choices, the correct option is "None of the above".

To minimize a difference expression (A - B) over a range, always use the absolute minimum of A and subtract the absolute maximum of B.

Answer: (d).

Question details

Year

2025

Paper

CSAT

Question

Q36

Section

Numerical Ability

Sub-topic

Inequalities & Ranges

Type

Algebra & equations

Difficulty

Medium

Source hint

Range arithmetic

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