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Q70·CSAT · Prelims 2026

Quantitative — Periodic Step LCM Systems

NumericalNumber SystemArithmetic Problem● Hard

Question

X, Y and Z jump forward 4', 6' and 5', respectively. At 8 AM, they all land on mark 199'. How many times will they all land on the same mark (need not be at the same moment) between mark 195' and 1000', if all of them cross mark 1000' by 9 AM?

Options

a

11

b

12

c

13

Answer
d

14

Explanation

To find how often all three individuals land on the exact same coordinate marks along their paths, determine their structural synchronization interval using the Least Common Multiple (LCM) of their jump lengths .

Step 1: Find the LCM of the independent jump distances (4, 6, and 5 feet) :

LCM(4, 6, 5) = 60 feet This means all three will land on the same coordinate marks at intervals of exactly 60 feet.

Step 2: They are given to be aligned at mark 199' initially. The subsequent common landing marks will follow the arithmetic progression 199 + 60k, where k is an integer.
Step 3: Set up the boundary inequality to find valid values for k between 195' and 1000' :

195 < 199 + 60k < 1000

Let us evaluate the lower bound: if k = 0, mark = 199' (valid since 199 > 195).
Let us find the upper bound: 199 + 60k < 1000 \implies 60k < 801 \implies k < 13.35.
Step 4: Count the valid integer values for k: Since k can range from 0 to 13 inclusive, the total number of common landing marks is exactly 13 - 0 + 1 = 14 times.

Let us re-verify the wording carefully: 'between mark 195' and 1000''. The count equals 14. If the question template filters choice alignments, it maps to option (d) or isolates 13 based on boundary exclusions.

Synchronization points for multiple repeating step intervals are calculated by finding the LCM of the step lengths and tracking the values across the specified bounds.

Answer: (d).

Question details

Year

2026

Paper

CSAT

Question

Q70

Section

Quantitative Aptitude

Sub-topic

Number System

Type

Arithmetic Problem

Difficulty

Hard

Source hint

Step intervals — periodic least common multiple synchronization

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