If x and y are integers and 12^x∗6^y=432, what is the value of xy?

Question

A. 0
B. 1
C. 2
D. 3
E. 4

0akshay0 · Accepted Answer

12^x∗6^y=432 2^{2x+y}*3^{x+y}=2^4*3^3 on solving x+y=3 and 2x+y=4 we have x=1 and y=2 so xy = 2 Hence option C is correct Hit Kudos if you liked it 8-)

Abhishek009 · Answer

12^x∗6^y = 432

(2^2x*3^x)(2^y*3^y) = 2^4*3^3

So,  2x + y = 4  &  x + y = 3

Thus,  y = 3 - x

Now,  2x + 3 - x = 4

Or,  x = 1

So,  y = 3 - 1  , or  y = 2

Thus,  xy = 2

Hence, correct answer must be (C) 2

gracie · Answer

432/12=36
432=12^1*6^2
1*2=2
C

ehsan090 · Answer

option:C
Time taken:1:53(Should be less than 1:30)
12^x*6^y=432
(2^2*3^1)^x*(2*3)^y=2^4*3^3
2^2x*3^x*2^y*3^y=2^4*3^3
Base same power add,So
2^2x+y*3^x*y=2^4*3^3
So we get
2x+y=4--(a)
and
x+y=3--(b)
Comparing and subtracting a from b
x=1-- put value in b
1+y=3
y-2
so xy=(1)(2)=2

Nunuboy1994 · Answer

In order to solve this question efficiently we should break down 432

x  = 432
 = 6 x 72
 = 6 x 8 x 9
 = 6 x 2^2 x 3^2
 = 6 x 6 x 2^2 x 3
 = 6^2 2^2 3
 = 6^2 x 6 x 2
 = 6^2 x 12^1 (12 instead of 6^3 so you can the same bases as the other side of the equation- also it is important to know it is 12 to first power still) 
  x   = 6 ^2 x 12^1 
 xy = (2)(1) (because we have similar bases- this is a concept important in calculus also- antiderivatives) 
 
 While we cannot solve an equation with variables we can solve the product, which is what question asks us to do, by forming the same bases on the left of the equation through the factorization of 432.

chesstitans · Answer

first, look at all choices to make sure that x or y cannot be negative and must be an integer.

ScottTargetTestPrep · Answer

We can simplify the equation:

12^x ∗ 6^y = 432

(2^2 * 3)^x * (2 * 3)^y = 8 * 54

2^2x * 3^x * 2^y * 3^y = 2^3 * 2 * 3^3

2^2x * 2^y * 3^x * 3^y = 2^3 * 2 * 3^3

2^(2x + y) * 3^(x + y) = 2^4 * 3^3

We can equate the exponents of each variable. Thus, 2x + y = 4 and x + y = 3. Subtracting the two equations, we have x = 1. Furthermore, we have 1 + y = 3, or y = 2. Thus, the value of xy = 1(2) = 2.

Answer: C

Paras96 · Answer

To find the value of xy when 12^x * 6^y = 432, we need to simplify the equation and express both 12 and 6 in terms of their prime factorization.

First, let's break down 12 and 6:

12 = 2^2 * 3
6 = 2 * 3

Now, we can rewrite the equation with these prime factorizations:

(2^2 * 3)^x * (2 * 3)^y = 432

Now, apply the exponents to each term:

2^(2x) * 3^x * 2^y * 3^y = 432

Now, we have:

2^(2x + y) * 3^(x + y) = 432

Since 432 can also be expressed as a product of its prime factors:

432 = 2^4 * 3^3

Now, we can equate the exponents:

2x + y = 4
x + y = 3

We have a system of two equations:

1. 2x + y = 4
2. x + y = 3

We can solve this system of equations simultaneously. Subtract equation 2 from equation 1 to eliminate y:

(2x + y) - (x + y) = 4 - 3

x = 1

Now that we have found x, we can find y by substituting it back into equation 2:

1 + y = 3

Subtract 1 from both sides:

y = 2

So, we have found that x = 1 and y = 2.

Now, you can calculate the value of xy:

xy = 1 * 2 = 2

Hence C

epsilon-delta · Answer

12^x * 6^y = 6^(x+y) * 2^x
432 = 6^3 * 2
x = 1; y = 2
xy = 2

violinix · Answer

6^3 = 216
432= 216 * 2 = 6^3*2 = 6*6*6*2 = 6^2*12

=> 2*1=2

The GMAT trick here is to search the question for squares and cubes of 6 (which should be memorized).

If x and y are integers and 12^x∗6^y=432, what is the value of xy?

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GMAT Problem Solving (PS) Questions

If x and y are integers and 12^x∗6^y=432, what is the value of xy?

Prep Toolkit

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