p, q, r and s are in AP such that p+s=8 and qr=15 . What is the difference between largest and smallest numbers?

Correct answer: A. 6 p, q, r, s in AP p+s=8 q+r=8 and q r=15 By observation, q and r can take values 3 or 5. The possible AP can be 1,3,5,7 or 7,5,3,1 . Difference =7-1=6 .

NDA 2023

Exam: NDA
Year: 2023
Subject: Mathematics
Chapter: Sequences and Series

NDA 2023 · Mathematics · Sequences and Series

p, q, r and s are in AP such that p+s=8 and qr=15 . What is the...

\mathrm{p}, \mathrm{q}, \mathrm{r}

and s are in AP such that

\mathrm{p}+\mathrm{s}=8

and

\mathrm{qr}=15

. What is the difference between largest and smallest numbers?

Options

A $6$
B $5$
C $4$
D $3$

Correct answer

A. $6$

Step-by-step solution

p, q, r, s

in AP

p+s=8\therefore \quad q+r=8

and

q r=15

By observation,

q

and

r

can take values 3 or 5.

\therefore \quad

The possible AP can be

1,3,5,7

7,5,3,1

\therefore \quad

Difference

=7-1=6

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