# CAT 2019 Quant Questions with Solutions

Question:
If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686,$ then x+y equals

Taking $2^{n d}$ equation

$5^{x-1}+3^{y+1}=9686$, the last digit of $5^{x-1}$ will always be 5 for all positive integral values of x

The power cycle of 3 is:

$3^{4 k+1} \equiv 3$

$3^{4 k+2} \equiv 9$

$3^{4 k+3} \equiv 7$

$3^{4 k} \equiv 1$

Clearly $3^{y+1}$ must be in the form of $3^{4 k}$ as the unit digit of R.H.S. =6

We have ${{3}^{4}}=81,\text{and}\ {{3}^{8}}=6561$

Also, $9686-81=9605$and $9686-6561=3125$

Observe that $3125=5^{5}$

Hence $5^{x-1}=5^{5}$

or $x=6$ and $3^{y+1}=3^{8} \Rightarrow y=7$

(x=6 and y=7 also satisfies the first equation)

Therefore, $x+y=6+7=13$

Get one day FREE Trial of CAT online Full course
Also Check: 841+ CAT Quant Questions with Solutions

#### CAT Quant Online Course

• 1000+ Practice Problems
• Detailed Theory of Every Topics
• Online Live Sessions for Doubt Clearing
• All Problems with Video Solutions

## Try CAT 2020 online course for 1 day for FREE

Please provide your details to get FREE Trial of Bodhee Prep's Online CAT Course for one day. We will inform you about the trial on your whatsApp number with the activation code.