If 3x4y = 177,147 and x – y = 11, then x =?

Question

If 3^x*4^y = 177,147 and x – y = 11, then x =?

A) Undefined
B) 0
C) 11
D) 177,136
E) 177,158

BrentGMATPrepNow · Accepted Answer

Great question, Brunuel!

Notice that, since 177,147 is ODD, it is not a multiple of 4. 
This means that y MUST equal zero. 
If y = 0 AND we know that x - y = 11, we can conclude that x = 11

Answer: C

Cheers,
Brent

viksingh15 · Answer

177147 does not contain any power of 2, that means y should be 0 => x=11

TeamGMATIFY · Answer

This is a question which needs your keen observation rather than calculation powers.
The first thought that comes into mind after looking at such questions is to factorize the number.

When we try to do that, we see that 177,147 is odd, therefore 4^y = 1 or y = 0
We have x - y = 11
Therefore x = 11

Option C

mejia401 · Answer

Good question. Y must be zero since 177,147 is without an even. This leaves X = 11 because the two others cannot be the powers of three since the 3^x*4^y = 177147 must be true. They would be too big. The number doesn't divide into 3 eleven times either therefore the answer must be irrational, so IMO A. undefined.

mejia401 · Answer

Aw dang, answer fail. I used the calculator shortly after answering the question. I wouldn't let myself not put my answer up first before doing so haha. The thing is, how could deduce that three divides into that number? I couldn't think of any quick tricks, and unless you have a trick, it's 50/50 (which isn't bad odds on this test though.. but still)

CrackverbalGMAT · Answer

If the base is odd, the final result will always be odd regardless of the exponent to which it is raised. Similarly, if the base is even, the final result will always be even regardless of the nature of the exponent.

This is based on the fact that exponentiation is repeated multiplication and repeatedly multiplying odd numbers will give you an odd result and vice-versa.

Considering the above,  3^x  *  4^y  = 177,147 can happen only if  4^y  is odd. If  4^y  was even, the product can never be 177,147 (an odd number). The only way in which  4^y  can be odd is when y=0. Remember, any number (other than ZERO itself) raised to the power of 0 equals 1.
 
Substituting the value of y=0 in the equation x-y = 11, we get x = 11. It’s not just a coincidence then that  3^{11}  = 177,147 ?

An alternative approach to solve this question could be to use the cyclicity of units digits of the power of 3, but only after figuring out that  4^y  has to be odd. The cyclicity of unit digits of 3 is 3,9,7 and 1. Since the number we have is a number ending with 7, the power should be of the form 4k+3 and this also points us towards the fact that x=11.

The correct answer option is C.

Hope that helps!

TheNightKing · Answer

You can take a good guess that there will be at least 3^2 in the term.

So keep on dividing by 9 and then by 3 if needed.

177,147 divided by 9 = 19683
19683 divided by 9 = 2187
Keep on dividing by 9 : 243,27,3
3 is divisible by 3.

So we got 5 9s and 1 3s. That's 11 3s. That means y is 0 and x is 11.

Option C

Abhishek009 · Answer

177,147 = 3^11

So,  3^x*4^y = 3^{11}  Or,  x = 11

Thus,  y = 0  ;  4^0 = 1

Hence,  x – y = 11 => 11 - 0 , Answer must be (C)

souvik19 · Answer

This is one of the smartest questions I saw today. This is one of those questions which anyone can solve, but the catch is can you solve this under 20 sec? 
There is a huge takeaway from this question.  You need to be mindful when solving GMAT question and cannot immediately jump into calculations (prime factorisation in this case) 
And now I am your fan  Bunuel

For those looking for an efficient solution, notice that "177147" is an odd number and hence "4" cannot be its factor. So "y" in "4^y" must be zero so that "4^y = 1". Then, since x-y = 11, x=11

BrushMyQuant · Answer

Given that  (3^x)(4^y) = 177,147  and  x – y = 11  and we need to find the value of x

(3^x)(4^y)  = 177,147 =  3^{11}  =  3^{11} * 4^0 
=>  (3^x)(4^y)  =  3^11 * 4^0 
=> x = 11, y = 0

So,  Answer will be C 
Hope it helps!

Watch the following video to learn the Basics of Exponents

https://www.youtube.com/watch?v=9la4tJI7ZiI

Malar95 · Answer

Okay, another situation of instant guess.
x & y are powers so D & E are out. x>y so B is out. Exhausted me considered A only to realize that its definitely out. Left with B.
Thanks to others for helping me understand it but I feel the answer options easily gives the answer away.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If 3x4y = 177,147 and x – y = 11, then x =?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If 3x4y = 177,147 and x – y = 11, then x =?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards