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Q73·CSAT · Prelims 2026

Quantitative — Linear Jump Equations

NumericalAlgebra — Linear EquationsArithmetic Problem● Easy

Question

A toy T jumps forward or backward. In each forward jump, it moves 5' forward whereas in each backward jump, it moves 2' backward. If in 31 jumps, T moves exactly 15' forward, then what is the difference of the number of forward and backward jumps?

Options

a

6

b

7

Answer
c

8

d

9

Explanation

Let f be the number of forward jumps and b be the number of backward jumps completed by the toy .

From the total jump count: The total number of jumps is 31 .

f + b = 31 \implies b = 31 - f \quad --- (Equation 1)

From the net displacement: Forward moves add 5 feet and backward moves subtract 2 feet, resulting in a net position of 15 feet forward[cite: 5182, 5183].

5f - 2b = 15 \quad --- (Equation 2)

Substitution and Solution: Substitute Equation 1 into Equation 2:

5f - 2(31 - f) = 15 \implies 5f - 62 + 2f = 15 7f = 15 + 62 \implies 7f = 77 \implies f = 11 forward jumps

Find Backward Jumps (⟨MATH⟩b⟨/MATH⟩):

b = 31 - 11 = 20 backward jumps

Calculate the Difference: Find the absolute difference between the two jump categories:

Difference = |b - f| = |20 - 11| = 9

Spliced step problems can be resolved efficiently by setting up two simple linear equations for the total count and net displacement and solving via substitution.

Answer: (d).

Question details

Year

2026

Paper

CSAT

Question

Q73

Section

Quantitative Aptitude

Sub-topic

Algebra — Linear Equations

Type

Arithmetic Problem

Difficulty

Easy

Source hint

Linear tracking — simultaneous integer variable solutions

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