If x and y are intergers, what is the value of xy?
(1) 5^x=11^y
(2) 2^x=4^y
OA: A
I can't seem to figure out how to approach the first prompt. Please help!
Interger question
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 30
- Joined: Thu Jan 17, 2008 5:38 pm
- Followed by:1 members
- GMAT Score:680
Yes the official answer is A.
I somehow figured out how to solve this question after posting here.
The only way 5^x=11^y is when x and y are both zero.
Therefore A is sufficient to solve the problem.
I somehow figured out how to solve this question after posting here.
The only way 5^x=11^y is when x and y are both zero.
Therefore A is sufficient to solve the problem.
1) 5^x = 11^y
for example take x= 1, 2 , 3, 4
correspondingly, 5^x=5, 25, 125, 625
similarly for y=1 , 2 , 3
11^y= 11, 121, 1331
it clearly indicates that the unit digit for 5^x will always be 5 and for 11^y will always be 1. So you can never get any non-zero value which says 5^x = 11^y.
We know that zero to the power of any number will be 1. So 5^0 =1, similarly 11^0=1.
So x=y=0, is the only solution for above statement to hold true (5^x = 11^y).
Statement 1 is SUFFICIENT.
I hope it helps.
for example take x= 1, 2 , 3, 4
correspondingly, 5^x=5, 25, 125, 625
similarly for y=1 , 2 , 3
11^y= 11, 121, 1331
it clearly indicates that the unit digit for 5^x will always be 5 and for 11^y will always be 1. So you can never get any non-zero value which says 5^x = 11^y.
We know that zero to the power of any number will be 1. So 5^0 =1, similarly 11^0=1.
So x=y=0, is the only solution for above statement to hold true (5^x = 11^y).
Statement 1 is SUFFICIENT.
I hope it helps.
- Rich@VeritasPrep
- GMAT Instructor
- Posts: 147
- Joined: Tue Aug 25, 2009 7:57 pm
- Location: New York City
- Thanked: 76 times
- Followed by:17 members
- GMAT Score:770
dongkim2 and EdWood:
First of all EdWood, kudos to you on your screenname. If nothing else, "Plan 9 From Outer Space" and "Glen or Glenda" provided fodder for Tim Burton's best movie.
But back to math...you guys have it right. 5^x = 11^y cannot be true unless both x and y are 0. I like EdWood's method of thinking about the units digits.
You can also consider prime factorization (my single favorite topic on the GMAT!)...
5^x will be some power of 5, since x is an integer, and any power of 5 breaks down into a prime factorization that includes only 5's (no 11's). Same with 11^y (no 5's as prime factors).
So the only way 5^x could possibly equal 11^y is if both x and y are 0, thus eliminating prime factors altogether.
blaster:
Applying the n-equations, n-variables rule is a great instinct to have, so it's great you've developed that. However, that rule applies strictly to LINEAR EQUATIONS. Because we're dealing with exponents here, the rule does not apply.
Another example would be quadratics. x^2 = 4 is a single equation with a single variable, but it produces two possible x values, because the equation is not linear.
Make sense?
First of all EdWood, kudos to you on your screenname. If nothing else, "Plan 9 From Outer Space" and "Glen or Glenda" provided fodder for Tim Burton's best movie.
But back to math...you guys have it right. 5^x = 11^y cannot be true unless both x and y are 0. I like EdWood's method of thinking about the units digits.
You can also consider prime factorization (my single favorite topic on the GMAT!)...
5^x will be some power of 5, since x is an integer, and any power of 5 breaks down into a prime factorization that includes only 5's (no 11's). Same with 11^y (no 5's as prime factors).
So the only way 5^x could possibly equal 11^y is if both x and y are 0, thus eliminating prime factors altogether.
blaster:
Applying the n-equations, n-variables rule is a great instinct to have, so it's great you've developed that. However, that rule applies strictly to LINEAR EQUATIONS. Because we're dealing with exponents here, the rule does not apply.
Another example would be quadratics. x^2 = 4 is a single equation with a single variable, but it produces two possible x values, because the equation is not linear.
Make sense?
Rich Zwelling
GMAT Instructor, Veritas Prep
GMAT Instructor, Veritas Prep