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# What is the value of the two-digit positive integer XY, where X repres

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Math Expert
Joined: 02 Sep 2009
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What is the value of the two-digit positive integer XY, where X repres  [#permalink]

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01 Jul 2018, 19:41
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67% (00:51) correct 33% (01:04) wrong based on 84 sessions

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What is the value of the two-digit positive integer XY, where X represents the tens digit and Y represents the units digit?

(1) The product of the digits is 12.

(2) The sum of the digits is 8.

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Joined: 27 Feb 2018
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Re: What is the value of the two-digit positive integer XY, where X repres  [#permalink]

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01 Jul 2018, 23:25
The order of number is not mentioned so m not sure if we can assume z as the last no. And x as first.... so i think it should be C

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Concentration: Accounting, Finance
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Re: What is the value of the two-digit positive integer XY, where X repres  [#permalink]

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01 Jul 2018, 23:42
Bunuel wrote:
What is the value of the two-digit positive integer XY, where X represents the tens digit and Y represents the units digit?

(1) The product of the digits is 12.

(2) The sum of the digits is 8.

The problem ask for the value of two-digit integer XY which its value is 10x+y
Given these following statements

(1) The product of the digits is 12.
From this statement x*y=12 which there are many possible combinations
ex. x=2 and y=6, x=3 and y=4, and so on ---> Insufficient

(2) The sum of the digits is 8
From this statement x+y=8 which there are many possible combinations
ex. x=1 and y=7, x=2 and y=6, and so on ---> Insufficient

Combined (1) & (2), we have 2 equations to solve for x and y
$$x+y=8$$
$$(x+y)^2=8^2$$
$$x^2+2xy+y^2=64$$
$$x^2+2*12+y^2=64$$
$$x^2+y^2=64-24$$
$$x^2+y^2=40$$
From these equations, the possible combinations are x=2 and y=6 or x=6 and y=2
These are still insufficient since the possible values of xy can be both 26 and 62

My answer is "E"
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Joined: 02 Aug 2009
Posts: 7095
Re: What is the value of the two-digit positive integer XY, where X repres  [#permalink]

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01 Jul 2018, 23:44
Bunuel wrote:
What is the value of the two-digit positive integer XY, where X represents the tens digit and Y represents the units digit?

(1) The product of the digits is 12.

(2) The sum of the digits is 8.

Priyanka8793,
you are correct as we do not know what will be the order but then answer will be E for this very reason and not C

XY..

(1) The product of the digits is 12.
number scan be 2 and 6 so 26 or 62
numbers can be 3 and 4 so 34 or 43
insuff

(2) The sum of the digits is 8
numbers can be 17, 71,26,62 etc
insuff

combined

possibility still can be 26 or 62
insuff

E
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the value of the two-digit positive integer XY, where X repres &nbs [#permalink] 01 Jul 2018, 23:44
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# What is the value of the two-digit positive integer XY, where X repres

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