Question

In a 3-digit number, the digit in the tenth place is the number 9, and the digit in the hundreds place is twice as big as the digit in the ones place. The possible number(s) is/are

• A. 492
• B. 294
• C. 693
• D. 369

Answer 1

Answer: (A), (C)

693

The number has 3 digits and the digit in the middle is 9 (Which is in the tenth place). So far the number looks like this: p9q

The digit in the hundreds place is p and the digit in the ones place is q.

As the digit in the hundreds place is twice as big as the digit in the ones place
$\therefore p=2q$

$\left(A\right)492$
Here, $p=4,q=2$
$\Rightarrow 2q=2\times 2=4=p$
$\to \text{ACCEPTED}$

$\left(B\right)294$
Here, $p=2,q=4$
$\Rightarrow 2q=2\times 4=8\ne p$
$\to \text{REJECTED}$

$\left(C\right)693$
Here, $p=6,q=3$
$\Rightarrow 2q=2\times 3=6=p$
$\to \text{ACCEPTED}$

$\left(D\right)369$
Here, $p=3,q=9$
$\Rightarrow 2q=2\times 9=18\ne p$
$\to \text{REJECTED}$

$\therefore$ The possible numbers are 492 or 693.