The question is incorrect
If 3x - 3x-1 = 162, this means -1 = 162.
Can you pls correct it
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Exponent question
Source: Beat The GMAT — Problem Solving |
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Brian@VeritasPrep
- GMAT Instructor
- Posts: 1031
- Location: Malibu, CA
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I love the question and rerika's attempt to post the exponents as actual exponents (rather than the x^y) form, but it didn't quite translate.
I think I can break down the question, though (and it fits with the answer choices). It should read:
If 3^x - 3^(x-1) = 162, then what is x(x-1)?
A) 12
B) 16
C) 20
D) 30
E) 81
As it's written, the answer is C.
Explanation (I'll put in "spoiler" text since many have not been able to read the question yet):
[spoiler]It may seem awkward to do, but you can factor out a 3^(x-1) from both terms on the left hand side. 3^x can be written as 3^1 * 3^(x-1) in order to create that duplicate term to factor:
3^x - 3^(x-1) = 162
3^1 * 3^(x-1) - 3^(x-1) = 162
[3^(x-1)] (3-1) = 162
[3^(x-1)] * 2 = 162
Then you can divide both sides by 2 to get:
3^(x-1) = 81
As with any exponent problem with variables in the exponents, you should try to create the same bases:
3^(x-1) = 3^4
x - 1 = 4
x = 5
x(x-1) = 5*4 = 20
That's one, fairly direct way to do it. Another way would be to recognize that you need to find 3s on the right hand side of the equation to be able to do anything with the 3^variable terms on the left, and factor 162 into 2*3^4. Then you could either backsolve combinations of x and x-1 or work to find patterns with 3s and consecutive exponents.
Ultimately, I'd say that the biggest takeaway on this problem is that, when exponents appear with variables in the exponents, you should try to find common bases, and usually to do that you'll want to break numbers down into prime factors. [/spoiler]
I think I can break down the question, though (and it fits with the answer choices). It should read:
If 3^x - 3^(x-1) = 162, then what is x(x-1)?
A) 12
B) 16
C) 20
D) 30
E) 81
As it's written, the answer is C.
Explanation (I'll put in "spoiler" text since many have not been able to read the question yet):
[spoiler]It may seem awkward to do, but you can factor out a 3^(x-1) from both terms on the left hand side. 3^x can be written as 3^1 * 3^(x-1) in order to create that duplicate term to factor:
3^x - 3^(x-1) = 162
3^1 * 3^(x-1) - 3^(x-1) = 162
[3^(x-1)] (3-1) = 162
[3^(x-1)] * 2 = 162
Then you can divide both sides by 2 to get:
3^(x-1) = 81
As with any exponent problem with variables in the exponents, you should try to create the same bases:
3^(x-1) = 3^4
x - 1 = 4
x = 5
x(x-1) = 5*4 = 20
That's one, fairly direct way to do it. Another way would be to recognize that you need to find 3s on the right hand side of the equation to be able to do anything with the 3^variable terms on the left, and factor 162 into 2*3^4. Then you could either backsolve combinations of x and x-1 or work to find patterns with 3s and consecutive exponents.
Ultimately, I'd say that the biggest takeaway on this problem is that, when exponents appear with variables in the exponents, you should try to find common bases, and usually to do that you'll want to break numbers down into prime factors. [/spoiler]
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
3^x - 3^x-1 =162rerika01 wrote:I am trying to figure out how to solve this question. Thanks
If 3^x - 3^x-1 =162, then x(x-1)=?
A) 12
B) 16
C) 20
D) 30
E) 81
factorise 162....
Right hand Side of the equation : 162 = 3^4 * 2
[spoiler]left Hand side of the equation :
3^x - 3^x-1 = 3^x(1 - 1/3) = 3^x * (2/3) = 3^(x-1) * 2
So,
3^(x-1) * 2 = 3^4 * 2
So (x-1) = 4 which implies x = 5
So (x-1)x = 4*5 = 20[/spoiler]
@Deb
Hey Brian,
I was actually thinking of this problem this way:
3^x - 3^(x-1) =162
3^x - 3^(x-1) = 3^4 + 3^4
Now I have the same bases, could I just take the exponents from here on?
x-(x-1)=4+4 <-- would this be right?
Thanks,
I was actually thinking of this problem this way:
3^x - 3^(x-1) =162
3^x - 3^(x-1) = 3^4 + 3^4
Now I have the same bases, could I just take the exponents from here on?
x-(x-1)=4+4 <-- would this be right?
Thanks,
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
- Alfred A. Montapert, Philosopher.
-
Brian@VeritasPrep
- GMAT Instructor
- Posts: 1031
- Location: Malibu, CA
- Thanked: 716 times
- GMAT Score:750
Hey Gurpinder,
I like the thought, but as you've probably noticed you end up with a nonsense equation from there:
x - (x-1) = 4+4
1 = 8 ----> Which is obviously not correct, and the xs are long gone.
The reason for that is that we can only strip off the bases if we have a one-for-one equality (like 3^(x-1) = 3^4). When addition or subtraction of exponents is present, we just don't have enough to be able to break off the exponents (a pretty important concept...we're really good at multiplication/division of exponents but terrible at adding/subtracting).
Think of it this way - we only add exponents when we're multiplying their bases. Here, we're adding/subtracting their bases, so we don't have any indication that we can combine the exponents. 3^4 + 3^4 is not 3^8...
Remember this - when using exponents, the majority of the rules we have are for multiplication/division of the same bases, so your goal should be to use factoring to get you in a position to use those rules.
I like the thought, but as you've probably noticed you end up with a nonsense equation from there:
x - (x-1) = 4+4
1 = 8 ----> Which is obviously not correct, and the xs are long gone.
The reason for that is that we can only strip off the bases if we have a one-for-one equality (like 3^(x-1) = 3^4). When addition or subtraction of exponents is present, we just don't have enough to be able to break off the exponents (a pretty important concept...we're really good at multiplication/division of exponents but terrible at adding/subtracting).
Think of it this way - we only add exponents when we're multiplying their bases. Here, we're adding/subtracting their bases, so we don't have any indication that we can combine the exponents. 3^4 + 3^4 is not 3^8...
Remember this - when using exponents, the majority of the rules we have are for multiplication/division of the same bases, so your goal should be to use factoring to get you in a position to use those rules.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank. Learn More.
I kind of had the feeling that I just got a meaningless equation right in the beginning!Brian@VeritasPrep wrote:Hey Gurpinder,
I like the thought, but as you've probably noticed you end up with a nonsense equation from there:
x - (x-1) = 4+4
1 = 8 ----> Which is obviously not correct, and the xs are long gone.
The reason for that is that we can only strip off the bases if we have a one-for-one equality (like 3^(x-1) = 3^4). When addition or subtraction of exponents is present, we just don't have enough to be able to break off the exponents (a pretty important concept...we're really good at multiplication/division of exponents but terrible at adding/subtracting).
Think of it this way - we only add exponents when we're multiplying their bases. Here, we're adding/subtracting their bases, so we don't have any indication that we can combine the exponents. 3^4 + 3^4 is not 3^8...
Remember this - when using exponents, the majority of the rules we have are for multiplication/division of the same bases, so your goal should be to use factoring to get you in a position to use those rules.
GREAT Tips!
Thanks Brian.
"Do not confuse motion and progress. A rocking horse keeps moving but does not make any progress."
- Alfred A. Montapert, Philosopher.
- Alfred A. Montapert, Philosopher.
3^x -3^(x-1)=3^(x)-3^(x)/3=2*3^4 or 3*3^x-3^x=2*3^5 or 2*3^x=2*3^5rerika01 wrote:I am trying to figure out how to solve this question. Thanks
If 3^x - 3^x-1 =162, then x(x-1)=?
A) 12
B) 16
C) 20
D) 30
E) 81
thus x= 5
and 5(5-1)=20
the answer is C
Good tips on using exponents...it's helpful to think of it that way that you should use factoring to get to a point where you can use the multiplication rules for exponents. Now that I think of it I've seen a lot of multiplication with exponents in practice but the addition/subtraction is harder, I guess because you have to turn it into multiplication to get it to work. Thanks!
Hi,
I did it as below:
3^x can be grouped as a unit as say y.
So the equation now becomes :
y - y/3 = 162.
Solving this gets me y = 243.
So y = 3^x = 243 which solves as to x =5.
x(x-1) = 5 X 4 = 20 (C)
I did it as below:
3^x can be grouped as a unit as say y.
So the equation now becomes :
y - y/3 = 162.
Solving this gets me y = 243.
So y = 3^x = 243 which solves as to x =5.
x(x-1) = 5 X 4 = 20 (C)
Sandy
Here is how I solved this:
3^x - 3^(x-1) = 162
3^x -(3^x)(3^-1)= 162
3^x(1-1/3)= 162
3^x(2/3)=162
3^x= 162 * 3/2
3^x = 81 * 3
x = 5
5 * (5-1) = 20
C. 20
3^x - 3^(x-1) = 162
3^x -(3^x)(3^-1)= 162
3^x(1-1/3)= 162
3^x(2/3)=162
3^x= 162 * 3/2
3^x = 81 * 3
x = 5
5 * (5-1) = 20
C. 20
