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# In a certain two-digit integer , the ration of the units

Author Message
Intern
Joined: 07 Sep 2008
Posts: 25
In a certain two-digit integer , the ration of the units [#permalink]

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03 Oct 2008, 12:35
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

In a certain two-digit integer , the ration of the units digit to the tens digit is 2 to 3. what is the integer?

1) the tens digit is 3 more than the units digit
2) the product of the two digits is 54.

Manager
Joined: 27 Sep 2008
Posts: 76

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03 Oct 2008, 13:12
given

10x+y = integer

y/x = 2/3

{2,3 or 4,6 or 6,9}

statement 1

only possible pair is {6,9}

statement 2

only possible pair is {6,9}

so I get (D)

Manager
Joined: 12 Feb 2008
Posts: 179

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03 Oct 2008, 13:17
i also get D.
Intern
Joined: 29 Sep 2008
Posts: 46

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03 Oct 2008, 15:30
i would have chosen D in the real test.
but if this is the answer and with this explanation I would call it a Geek question:

1 and 2 individually let you determine the digits of the integer, but even together they do not tell you the sign.

it could be 96 or -96

thus E
Intern
Joined: 07 Sep 2008
Posts: 25

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03 Oct 2008, 16:01
i think it's E because both statements lead to 96 and -96
Manager
Joined: 27 Sep 2008
Posts: 76

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03 Oct 2008, 21:53
andreasonlinegr wrote:
i think it's E because both statements lead to 96 and -96

if true, this is the worse problem ever.

SVP
Joined: 05 Jul 2006
Posts: 1747

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04 Oct 2008, 02:47
andreasonlinegr wrote:
In a certain two-digit integer , the ration of the units digit to the tens digit is 2 to 3. what is the integer?

1) the tens digit is 3 more than the units digit
2) the product of the two digits is 54.

a+10b , 10b/a = 2/3 thus

30b = 2a ie: 15b = a rewriting the number : 15b+10b = 25b

from 1

a= 3+b....insuff ( we need b)

from 2

ab = 54 = 2*3^3 ......insuff( multiple values)

both

3b+b^2 = 54 thus b^2+3b+54v= 0

(b+6)(b+9) = 0 thus b could be either -6 or -9...insuff
E
Intern
Joined: 22 Dec 2007
Posts: 5

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04 Oct 2008, 06:38
Unit digit : tenth digit = 2 : 3 means tenth digit is 1.5 times (3/2=1.5) of unit digit. but -9 could not be 1.5 times of 6.

so i don't agree with the ans E

I think the answer is D...........
Manager
Joined: 22 Sep 2008
Posts: 122

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04 Oct 2008, 09:21
they are talking about digits not digit with their sign

-96 = 96 * 10^-1

-960 = 960 * 10^-1

so you can never associate - sign with unit or tens or hundred digit..
SVP
Joined: 17 Jun 2008
Posts: 1547

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05 Oct 2008, 13:47
Good one. What is the source of this problem?
Manager
Joined: 12 Feb 2008
Posts: 179

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05 Oct 2008, 15:21
this is the trickiest question ever.
Intern
Joined: 07 Sep 2008
Posts: 25

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06 Oct 2008, 16:01
this question came from a gmat school in athens, greece

thank you all for your responses
VP
Joined: 18 May 2008
Posts: 1261

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06 Oct 2008, 19:07
So does that mean, in such questions we should look for statement a positive 2 digit number? In questions done so far, i have neve cum across this
Re: ration   [#permalink] 06 Oct 2008, 19:07
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