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# If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di

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Manager
Joined: 30 May 2018
Posts: 61
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di  [#permalink]

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21 Apr 2019, 03:55
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Difficulty:

45% (medium)

Question Stats:

59% (01:31) correct 41% (01:51) wrong based on 27 sessions

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If two 2-digit integers consist of 6, 7, 8, and 9, with each of the digits using exactly once, what is the greatest value of product of two integers?

(A) 5,963
(B) 7,448
(C) 8,342
(D) 8,352
(E) 8,613

Manager
Joined: 05 Oct 2017
Posts: 67
Re: If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di  [#permalink]

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21 Apr 2019, 04:13
i started with combinations of maximizing the highest number, tried out 97 *86 = 8342
then tried 96 * 87 = 8352
also tried 98 * 76 = 7548.
looks like just maximizing one number won't help, both should reach as close as possible.
Any time-efficient approach for this question would be appreciated.
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Intern
Joined: 16 Jan 2019
Posts: 49
Location: India
Concentration: General Management, Strategy
WE: Sales (Other)
Re: If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di  [#permalink]

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21 Apr 2019, 04:36
The product of two numbers is maximized when their difference is minimized.

Posted from my mobile device
Senior Manager
Joined: 19 Oct 2018
Posts: 298
Location: India
Re: If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di  [#permalink]

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21 Apr 2019, 06:29
1
First try to maximize the product of tens digits of both numbers (In this case it's possible when one number has tens digit 9 and other number has tens digit 8)
Then try to minimize the difference of two numbers (in this case 96-87=9 is minimum)
neha283 wrote:
i started with combinations of maximizing the highest number, tried out 97 *86 = 8342
then tried 96 * 87 = 8352
also tried 98 * 76 = 7548.
looks like just maximizing one number won't help, both should reach as close as possible.
Any time-efficient approach for this question would be appreciated.
Manager
Joined: 30 May 2018
Posts: 61
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
Re: If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di  [#permalink]

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21 Apr 2019, 07:02
firas92 wrote:
The product of two numbers is maximized when their difference is minimized.

Posted from my mobile device

Then what is wrong with 69*78.

78 - 69 = 9

Although, its product (6,003) is not in the option. But is every tedious task first to identify different numbers, then to calculate difference between all 12 different numbers and then multiply the ones with lowest difference.

Any other better way ? Anybody ?
Intern
Joined: 16 Jan 2019
Posts: 49
Location: India
Concentration: General Management, Strategy
WE: Sales (Other)
Re: If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di  [#permalink]

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21 Apr 2019, 07:57
MBA20 wrote:
firas92 wrote:
The product of two numbers is maximized when their difference is minimized.

Posted from my mobile device

Then what is wrong with 69*78.

78 - 69 = 9

Although, its product (6,003) is not in the option. But is every tedious task first to identify different numbers, then to calculate difference between all 12 different numbers and then multiply the ones with lowest difference.

Any other better way ? Anybody ?

Sorry, I should've been clearer with my explanation.

A good way to start will be to maximize the tens digits of both numbers first like nick1816 has mentioned. So we'll have (96,87) or (97,86) and from this we can choose the pair with the smaller difference that is (96,87)

Hope its clear.
Manager
Joined: 12 Sep 2017
Posts: 247
Re: If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di  [#permalink]

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21 Apr 2019, 18:19
You can think about in geometry!

When does the area of the rectangle have the greatest area?

When the sides are equal, so try to have more equal numbers:

96 * 87

D
Re: If two 2-digit integers consist of 6, 7, 8, and 9, with each of the di   [#permalink] 21 Apr 2019, 18:19
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