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# Which is greater 98^7/7^{63} or 2^7/7^{49}

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Which is greater 98^7/7^{63} or 2^7/7^{49} [#permalink]  03 Jun 2017, 01:45
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Question Stats:

62% (00:52) correct 37% (00:55) wrong based on 181 sessions

 Quantity A Quantity B $$\frac{98^7}{7^{63}}$$ $$\frac{2^7}{7^{49}}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: 98^7 [#permalink]  27 Sep 2017, 05:05
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Column A can be rewritten as $$\frac{7^{14}2^7}{7^{63}}=\frac{2^7}{7^{49}}$$. Thus, column A and B are equal and answer is C!
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Re: 98^7 [#permalink]  27 Sep 2017, 05:47
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IlCreatore wrote:
Column A can be rewritten as $$\frac{7^{14}2^7}{2^{63}}=\frac{2^7}{7^{49}}$$. Thus, column A and B are equal and answer is C!

The ans should be -

Column A & Column B is

$$\frac{{7^{14}2^7}}{{7^{63}}}=\frac{{2^7}}{{7^{49}}}$$

which comes to option C
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Director
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Re: 98^7 [#permalink]  28 Sep 2017, 04:43
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pranab01 wrote:
IlCreatore wrote:
Column A can be rewritten as $$\frac{7^{14}2^7}{2^{63}}=\frac{2^7}{7^{49}}$$. Thus, column A and B are equal and answer is C!

The ans should be -

Column A & Column B is

$$\frac{{7^{14}2^7}}{{7^{63}}}=\frac{{2^7}}{{7^{49}}}$$

which comes to option C

You are right, I made a typo!
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Re: 98^7 [#permalink]  06 Oct 2017, 15:07
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Expert's post
Carcass wrote:

 Quantity A Quantity B $$\frac{98^7}{7^{63}}$$ $$\frac{2^7}{7^{49}}$$

We can solve this question using matching operations

Given:
Quantity A: (98^7)/(7^63)
Quantity B: (2^7)/(7^49)

Multiply both quantities by 7^63 to get:
Quantity A: 98^7
Quantity B: (2^7)(7^14)

Rewrite 7^14 as (7^7)(7^7) to get:
Quantity A: 98^7
Quantity B: (2^7)(7^7)(7^7)

A nice rule says (a^k)(b^k) = (ab)^k

Apply this rule to quantity B to get:
Quantity A: 98^7
Quantity B: (2 x 7 x 7)^7

Simplify to get:
Quantity A: 98^7
Quantity B: 98^7

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Manager
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Re: 98^7 [#permalink]  18 May 2018, 02:35
IlCreatore wrote:
Column A can be rewritten as $$\frac{7^{14}2^7}{7^{63}}=\frac{2^7}{7^{49}}$$. Thus, column A and B are equal and answer is C!

Nice .. it was hard to imagine that.. great
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Re: Which is greater 98^7/7^{63} or 2^7/7^{49} [#permalink]  19 Jun 2019, 13:15
How do you go from 98^7 to 7^14*2^7?
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Re: Which is greater 98^7/7^{63} or 2^7/7^{49} [#permalink]  19 Jun 2019, 13:28
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Expert's post
giancarlojr wrote:
How do you go from 98^7 to 7^14*2^7?

We use the rule that says $$(abc)^n = a^nb^nc^n$$

$$98 = (7)(7)(2)$$

So, $$98^7 = [(7)(7)(2)]^7$$

So, according to the above rule, we can write: $$98^7 = (7^7)(7^7)(2^7)$$

Since $$(7^7)(7^7) = 7^{14}$$, we can write: $$98^7 = (7^{14})(2^7)$$

Does that help?
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Re: Which is greater 98^7/7^{63} or 2^7/7^{49} [#permalink]  19 Jun 2019, 13:30
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that's perfect thanks!
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Re: Which is greater 98^7/7^{63} or 2^7/7^{49} [#permalink]  19 Jun 2019, 14:23
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Thank you greenlight test prep. best explanation!
Re: Which is greater 98^7/7^{63} or 2^7/7^{49}   [#permalink] 19 Jun 2019, 14:23
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