CAT 2026 · Slot 1 · Expected paper

CAT 2026 › Slot 1 paper › Quant

CAT 2026 Slot 1 Quant: Modern Maths Questions with Solutions

3 questions: Q14, Q17, Q21. Solve each one here: tap the answer, press Check, then open the solution.

Question 14Progressions

MCQ · +3 / −1

The number of common terms in the two sequences $18, 24, 30, 36, \ldots, 606$ and $14, 24, 34, 44, \ldots, 604$ is:
Answer and solution

Correct answer: C

Solution

First common term = 24; LCM(6,10) = 30. Common terms: 24, 54, 84, ..., up to min(606, last term of 2nd seq). Last term of 2nd seq: $14+10k\le606\Rightarrow k\le59.2$. Last: 604. Common terms up to 604: $\lfloor(604-24)/30\rfloor+1=20$

Question 17Logarithms

MCQ · +3 / −1

If $z$ is a negative number such that $2^{\,z^2 \log_5 7} = 7^{\log_2 5}$, then $z$ equals:
Answer and solution

Correct answer: B

Solution

Take $\log_2$ of both sides: $z^2 \log_5 7 = \log_2 5 \cdot \log_2 7$.
Since $\log_5 7 = \dfrac{\log_2 7}{\log_2 5}$, substitute: $z^2 \cdot \dfrac{\log_2 7}{\log_2 5} = \log_2 5 \cdot \log_2 7$.
Divide both sides by $\log_2 7$: $\dfrac{z^2}{\log_2 5} = \log_2 5 \Rightarrow z^2 = (\log_2 5)^2$.
Since $z$ is negative: $z = -\log_2 5 = \log_2\tfrac{1}{5}$.

Question 21Inequalities

TITA (type the answer) · +3 / 0

How many integers $n$ satisfy $(n - 3)(n - 6) - 3(n - 3) \le 0$?
Answer and solution

Correct answer: 7

Solution

$(n-3)(n-9)\le0\Rightarrow3\le n\le9$. Integers: 3,4,5,6,7,8,9 = $7$

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