# CAT 2023 Question Paper | Quant Slot 3

###### CAT Previous Year Paper | CAT Quant Questions | Question 2

CAT 2023 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like Speed-time-distance, Mixture and Alligations. This year, there was a surprise. The questions from Geometry were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 2 : Let $n$ and $m$ be two positive integers such that there are exactly 41 integers greater than $8^m$ and less than $8^n$, which can be expressed as powers of 2 . Then, the smallest possible value of $n+m$ is

1. 14
2. 42
3. 16
4. 44

## Best CAT Coaching in Chennai

#### CAT Coaching in Chennai - CAT 2022Limited Seats Available - Register Now!

We need to have 41 integers that can be expressed as powers of 2 between 8m and 8n.
That is we need to have 41 integers that can be expressed as powers of 2 between 23m and 23n.
The numbers will be of the form: $2 ^ { 3 m } , 2 ^ { 3 n + 1 } , 2 ^ { 3 m + 2 } , 2 ^ { 3 m + 3 } , $ldots , 2 ^ { 3 m + 41 } , 2 ^ { 3 n }$ clearly, $$quad 3 n - 1 = 3 m + 41$ $3$ n - m$ = 42$
$n - m = 14$
The smallest value $m$ can take $= 1$, then $n = 15$
$m + n = 1 + 15 = 16$

The question is " Let $n$ and $m$ be two positive integers such that there are exactly 41 integers greater than $8^m$ and less than $8^n$, which can be expressed as powers of 2 . Then, the smallest possible value of $n+m$ is "

Choice C is the correct answer.

###### CAT Coaching in ChennaiCAT 2024

Classroom Batches Starting Now! @Gopalapuram and @Anna nagar

###### Best CAT Coaching in Chennai

Attend a Demo Class

## CAT Questions | Verbal Ability for CAT

##### Where is 2IIM located?

2IIM Online CAT Coaching
A Fermat Education Initiative,
58/16, Indira Gandhi Street,
Kaveri Rangan Nagar, Saligramam, Chennai 600 093

##### How to reach 2IIM?

Mobile: (91) 99626 48484 / 94459 38484
WhatsApp: WhatsApp Now
Email: info@2iim.com