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Manager  Joined: 11 Mar 2010
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If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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Question Stats: 82% (02:03) correct 18% (02:27) wrong based on 316 sessions

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If $$\frac{(6^2)(44)(5^x)(20)}{(8^2)(9)} = 1375$$, what is the value of x?

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

Originally posted by lifeisshort on 20 Aug 2010, 11:12.
Last edited by Bunuel on 04 Nov 2014, 10:00, edited 5 times in total.
Edited the question.
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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If just looked at 5 then we have 5^(x+1) = 5^3

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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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mainhoon wrote:

If just looked at 5 then we have 5^(x+1) = 5^3

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How can we assume five-to-the-x-power, (5^x), is actually 5^x plus "some other number"? If that was the intention of the problem, then the problem would show (5^(x+1)) not (5^x)...right?

And in anycase, how did you decide on the answer choice? How do you know what the answer is....

Originally posted by lifeisshort on 20 Aug 2010, 11:28.
Last edited by lifeisshort on 20 Aug 2010, 11:31, edited 1 time in total.
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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I got the extra 5 from 20. I wa isolating all the 5s in one place.. So is it 2?

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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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I don't know the answer, unfortunately. Anyone able to offer a solution/explanation for this problem?
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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Ok so I took a calculator out and here is the bottom-line
5^x = 18.59, it's not a clean figure, I don't know why
But closest has to be 2..

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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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Ooops, I must apologize because I made a blunder in my copy/paste of this equation.
(62) should be (6^2), six-to-the-power-of-two.

So, does this change your answer...if not, can you elaborate more on how exactly you arrived at your solution? THanks. Joined: 03 Aug 2010
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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Are you sure that the denominator is correct? 1,375 factors to 11 * 5^3. The denominator factors to 41*2*3*3. There is no other 41 in the equation to cancel out. Further, 41 is a prime number. It just seems to me that this is the sort of problem where most other numbers will cancel out and you would be left with 5^x = 5^3.
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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I would say x is still 2 as your correction did not introduce any more 5s... Doublecheck with calc but 6^2 still doesn't work

lifeisshort wrote:
Ooops, I must apologize because I made a blunder in my copy/paste of this equation.
(62) should be (6^2), six-to-the-power-of-two.

So, does this change your answer...if not, can you elaborate more on how exactly you arrived at your solution? THanks.

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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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runnergirl683 wrote:
Are you sure that the denominator is correct? 1,375 factors to 11 * 5^3. The denominator factors to 41*2*3*3. There is no other 41 in the equation to cancel out. Further, 41 is a prime number. It just seems to me that this is the sort of problem where most other numbers will cancel out and you would be left with 5^x = 5^3.

Gosh, yes I see the denominator was incorrect; it should be (8^2), I made the change.
The problem is now correct....and with a quick calculator check, the answer should be 2 (answer D).

But is there anyway to do this OTHER than doing ALL of that LONG-hand multiplication and LONG-hand division? It takes too much time and increases the chance I'll make an error.

What is the shortcut?
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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Well, as I have been saying in my earlier posts above the shortest method indeed is:
5^(x+1) = 5^3
x=>2

Just compare the powers of 5 on both sides. I can't imagine anything shorter than this.
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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5
2
The attached should help.
Attachments solution.jpg [ 636.2 KiB | Viewed 5155 times ]

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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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seekmba wrote:
The attached should help.

Yup, that's how I did it. I think what we must remember in this case is that most of the time, GMAT problems that appear to require complex calculations can often be simplified to very manageable proportions.
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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You can do it two ways Either by solving the whole equation or by considering 1375 and it's factor with the factors on the other side
for full explanation Seekmba has given right but long explanation
another the shorter version
The whole equation on the left side when solved should be equal to the 1375
the factors of 1375 are 5*5*5*11
that means all this value will be present on the left side of the equation
and rest all will cancel each other out
Moreover we are not concerned about any powers of 2,3 and 11
we are only concerned with the power of 5
so we will search for the 5 as factor for the equation on the left
it comes out to be 5^x and 5 as a factor of 20
Hence 5^x*5 = 5^3
that is all what is required therefore the answer for x is 2
i.e. D
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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easy one if you prime factorise every term with 2 and 3 , just discard all possible and you are left with only one prime "5" to be operated
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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$$\frac{6^2* 44* 5^x *20}{8^2 *9} = 1375$$

$$5^{x+1} = 125$$

x+1 = 3

x = 2

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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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PareshGmat wrote:
$$\frac{6^2* 44* 5^x *20}{8^2 *9} = 1375$$

$$5^{x+1} = 125$$

x+1 = 3

x = 2

Can you explain this? Can't get it Math Expert V
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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neowacka wrote:
PareshGmat wrote:
$$\frac{6^2* 44* 5^x *20}{8^2 *9} = 1375$$

$$5^{x+1} = 125$$

x+1 = 3

x = 2

Can you explain this? Can't get it Explained here: if-6-2-44-5-x-20-8-2-9-1375-what-is-the-value-of-x-99494.html#p768504
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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I think we need to know the prime factors of 1375 then we must cancel out any prime factor different from the other side and complete the missing power of common prime factors.
1375 = 11 x 5 power 3 so there is no need for 2 or 3 on the other side. so 5 and 11 must have missing power which is 5 power 2
x = 2
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Re: If (6^2)(44)(5^x)(20) / (8^2)(9) = 1375, what is the value of x?  [#permalink]

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