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X is a two-digit positive integer. If the ratio between the units digi

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Bunuel
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X is a two-digit positive integer. If the ratio between the units digi [#permalink] New post   24 Jun 2016, 03:10
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X is a two-digit positive integer. If the ratio between the units digit and the tens digit is 1 to 2, what is the value of X?

(1) The sum of the digits multiplied by the tens digit is 54.
(2) The product of the digits divided by 2 is 9.
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LogicGuru1
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X is a two-digit positive integer. If the ratio between the units digi [#permalink] New post   Updated on: 25 Jun 2016, 14:25
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Bunuel wrote:
X is a two-digit positive integer. If the ratio between the units digit and the tens digit is 1 to 2, what is the value of X?

(1) The sum of the digits multiplied by the tens digit is 54.
(2) The product of the digits divided by 2 is 9.


\(\frac{UNIT}{TENS} = \frac{1}{2}\)

so the digits can be \(\frac{4}{8}\) or \(\frac{3}{6}\) or \(\frac{2}{4}\) or \(\frac{1}{2}\) (QUESTION STEM)
Number can be 84,63,42,21

(1) The sum of the digits multiplied by the tens digit is 54
(6+3) x 6=54=> number is 63

(2) The product of the digits divided by 2 is 9
\(\frac{(6 x 3)}{2}=9\)

THE ANSWER IS D

Originally posted by LogicGuru1 on 24 Jun 2016, 03:17.
Last edited by LogicGuru1 on 25 Jun 2016, 14:25, edited 1 time in total.
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Re: X is a two-digit positive integer. If the ratio between the units digi [#permalink] New post   25 Jun 2016, 01:19
Answer is D

Possible out comes of X could be : 42,63,84 since here the ratio between unit and tenth digit is 1/2

data 1 says that the sum of unit and ten digit TIMES to ten digit is 54 . Here , the only option which yields 54 under this condition is 63 since (6+3) *6 =54

so here the answer is clearly 63 and this data is sufficient.

data 2 says that unit*ten/2 =18 So here 6*3/2 = 9 and only answer here is 63 too and this data is sufficient too

1 & 2 are both sufficient and answer is D :P
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Re: X is a two-digit positive integer. If the ratio between the units digi [#permalink] New post   25 Jun 2016, 04:26
I will go with D

if the tens digit is : B and units Digit is A

a/b = 1/2

A and B
1 2
2 4
3 6
4 8

only 3 and 6 satsify both the conditions independently
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X is a two-digit positive integer. If the ratio between the units digi [#permalink] New post   25 Jun 2016, 14:21
mehrdadtaheri92 wrote:
Answer is D

Possible out comes of X could be : 42,63,84 since here the ratio between unit and tenth digit is 1/2

data 1 says that the sum of unit and ten digit TIMES to ten digit is 54 . Here , the only option which yields 54 under this condition is 63 since (6+3) *6 =54

so here the answer is clearly 63 and this data is sufficient.

data 2 says that unit*ten/2 =18 So here 6*3/2 = 9 and only answer here is 63 too and this data is sufficient too

1 & 2 are both sufficient and answer is D :P


you forgot 21.. such small mistakes can be fatal on GMAT
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Re: X is a two-digit positive integer. If the ratio between the units digi [#permalink] New post   25 Jun 2016, 19:44
Bunuel wrote:
X is a two-digit positive integer. If the ratio between the units digit and the tens digit is 1 to 2, what is the value of X?

(1) The sum of the digits multiplied by the tens digit is 54.
(2) The product of the digits divided by 2 is 9.


let unit digit =x , tens digit= 2x

St-1 (x+2x)*2x=54
6(x^2)=54
x=3
Sufficient

St- 2x*x/2=9
x^2=9
x=3
Sufficient

Ans. D
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AbhijitGoswami
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Re: X is a two-digit positive integer. If the ratio between the units digi [#permalink] New post   13 Nov 2016, 03:51
Hi All,

In this problems X is a two-digit positive integer sometimes we consider X as 10a+b , or a , b.
In this case I considered X as 10a+b, which is wrong. Any assumptions needed ??
-Regards,
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Re: X is a two-digit positive integer. If the ratio between the units digi [#permalink] New post   27 Jan 2021, 09:06
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Re: X is a two-digit positive integer. If the ratio between the units digi [#permalink]
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