## Quant Question Of The Day: 90

**Numbers**

**For how many values of natural number n, both the numbers 48n + 4 and 27n + 19 are perfect square?**

**(1) 0**

**(2) 1**

**(3) 2**

**(4) 3**

**(5) more than 3 **

**See our previous ‘Questions of the Day’: **

### 5 Comments

### Post your comment

(2) 1.

What approach did you use ?

48n+4=a^2

27n+19=b^2.

n=(a^2-4)/48 = (b^2-19)/27.

16b^2-9a^2=268.

only one pair of (a,b) satisfies the given two equations.

(2) 1

only possible value is n=10