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# If (2x)(7y)145(2x)(7y)145 = 983983, then x + y =

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If (2x)(7y)145(2x)(7y)145 = 983983, then x + y =  [#permalink]

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21 Aug 2018, 11:10
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Difficulty:

15% (low)

Question Stats:

83% (01:57) correct 17% (02:22) wrong based on 38 sessions

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If $$\frac{(2^x)(7^y)}{14^5}$$ = $$98^3$$, then $$x + y$$ =

1. 11

2. 14

3. 15

4. 19

5. 20

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Re: If (2x)(7y)145(2x)(7y)145 = 983983, then x + y =  [#permalink]

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21 Aug 2018, 11:58
AkshdeepS wrote:
If $$\frac{(2^x)(7^y)}{14^5}$$ = $$98^3$$, then $$x + y$$ =

1. 11

2. 14

3. 15

4. 19

5. 20

$$98 =7^2*2$$

So, $$98^3 =7^6*2^3$$

Agin, $$\frac{(2^x)(7^y)}{14^5}$$ = $$7^6*2^3$$

Or, $$\frac{(2^x)(7^y)}{7^5*2^5}$$ = $$7^6*2^3$$

Or, $$(2^x)(7^y)$$ = $$7^{11}*2^8$$

So, $$x = 8$$ and $$y = 11$$

Thus, $$x + y = 19$$ , Answer must be (4)
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If (2x)(7y)145(2x)(7y)145 = 983983, then x + y =  [#permalink]

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22 Aug 2018, 00:01

Solution

Given:
• $$\frac{(2^x)(7^y)}{14^5}$$ = $$98^3$$

To find:
• The value of (x + y)

Approach and Working:
If we simplify the given expression, we get
• $$\frac{(2^x)(7^y)}{14^5}$$ = $$98^3$$
Or, $$\frac{(2^x)(7^y)}{(2^5)(7^5)}$$ = $$2^3 * 7^6$$
Or, $$(2^{x-5})(7^{y-5})$$ = $$2^3 * 7^6$$

Comparing both sides of the equation, we get
• (x – 5) = 3
Or, x = 8

• (y – 5) = 6
Or, y = 11

• Hence, (x + y) = 8 + 11 = 19

Hence, the correct answer is option 4(D).

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If (2x)(7y)145(2x)(7y)145 = 983983, then x + y =   [#permalink] 22 Aug 2018, 00:01
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