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555-605 (Medium)|   Algebra|   Exponents|         
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GMATNinja
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 17 Apr 2022, 23:54
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Difficulty:

35% (medium)

Question Stats:

75% (02:17) correct 25% (02:30) wrong based on 550 sessions

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If \(x\) and \(y\) are integers and \(\frac{7^{x+1} - 7^{x-1}}{3}=(2^y)(49^6)\) what is the value of \(xy\)?

(A) 104
(B) 96
(C) 52
(D) 48
(E) 44
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C
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 17 Nov 2022, 08:01
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IN2MBB2PE
GMATNinja - I think you guys created this question for the Ukrain marathon but I cannot get to make headwind with this one, is there any solution? The posted solution are all over the place, I wonder if this question is correct, thanks!
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I think it's hard to read explanations to exponent questions when they're typed, so here you go:
Attachment:
IMG-6549.jpg
IMG-6549.jpg [ 2.25 MiB | Viewed 5873 times ]
The key is factoring in that very first step. It doesn't FEEL quite right, but think about what you do when you factor something simpler, like (x^8 + x^6). You'd factor out the smaller of the two terms, right?

Same thing here. Once you recognize how to factor out the 7^(x-1), the whole question gets easier quickly.

I hope that helps!
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 18 Apr 2022, 01:24
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GMATNinja
If \(x\) and \(y\) are integers and \(\frac{7^{x+1} - 7^{x-1}}{3}=(2^y)(49^6)\) what is the value of \(xy\)?

(A) 104 (B) 96 (C) 52 (D) 48 (E) 44
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\([fraction]7^{x+1} - 7^{x-1}[/fraction]=(3)(2^y)(49^6)\)
in RHS 7^12
LHS x=13 we get power same as 7^12 (7^2-1) ; 7^12*2^4*3
we get

7^12*2^4*3= 3*2^y *7^12
y will be 4

so x*y ; 13*4 ; 52
option C
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 19 Apr 2022, 11:14
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GMATNinja
If \(x\) and \(y\) are integers and \(\frac{7^{x+1} - 7^{x-1}}{3}=(2^y)(49^6)\) what is the value of \(xy\)?

(A) 104 (B) 96 (C) 52 (D) 48 (E) 44

\([fraction]7^{x+1} - 7^{x-1}[/fraction]=(3)(2^y)(49^6)\)
in RHS 7^12
LHS x=13 we get power same as 7^12 (7^2-1) ; 7^12*2^4*3
we get

7^12*2^4*3= 3*2^y *7^12
y will be 4

so x*y ; 13*4 ; 52
option C
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How you got x=13

how you got x=13?
how can we campare numerator with rhs of 7 ^12 only ...?
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samarth1222
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 05 Aug 2022, 20:33
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hi
can someone please provide the explanation for this question? I didn't understand the given solution
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harshittahuja
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 05 Aug 2022, 20:40
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If xx and yy are integers and 7x+1−7x−13=(2y)(496)7x+1−7x−13=(2y)(496) what is the value of xyxy?
solution
(7^(x+1)-7^(x-1))/3=2^y(49)^6
=7^(x-1)(49-1)/3==2^y(49)^6
=7^(x-1)(48)/3=2^y(49)^6
=7^(x-1)(16)=2^y(49)^6
=here by comparing both sides
y=4,x-1=12
y=4,x=13
xy=52
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 16 Nov 2022, 15:46
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GMATNinja - I think you guys created this question for the Ukrain marathon but I cannot get to make headwind with this one, is there any solution? The posted solution are all over the place, I wonder if this question is correct, thanks!
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 21 Nov 2022, 02:02
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how did we get 7^x-1 . 7^2 -1 ?
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Bunuel
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 21 Nov 2022, 02:08
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how did we get 7^x-1 . 7^2 -1 ?
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Express \(7^{(x + 1)}\) as \(7^2*7^{(x - 1)}\):

\(7^{(x + 1)} - 7^{(x - 1)} =\\
\\
= 7^2*7^{(x - 1)} - 7^{(x - 1)} = \\
\\
= 7^{(x - 1)}(7^2 - 1) = \)

Hope it's clear.
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If x and y are integers and 7^(x + 1) - 7^(x - 1) 04 Sep 2025, 13:47
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