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# Let x and y be two distinct digits in the decimal x.yx, what is x?

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Math Expert
Joined: 02 Sep 2009
Posts: 51280
Let x and y be two distinct digits in the decimal x.yx, what is x?  [#permalink]

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15 Jan 2017, 08:19
2
3
00:00

Difficulty:

75% (hard)

Question Stats:

52% (02:20) correct 48% (01:39) wrong based on 114 sessions

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Let x and y be two distinct digits in the decimal x.yx, what is x?

(1) When rounded to the nearest integer, the decimal becomes y
(2) When rounded to the nearest tenth, the decimal becomes x.y

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Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: Let x and y be two distinct digits in the decimal x.yx, what is x?  [#permalink]

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15 Jan 2017, 12:55
3
Bunuel wrote:
Let x and y be two distinct digits in the decimal x.yx, what is x?

(1) When rounded to the nearest integer, the decimal becomes y
(2) When rounded to the nearest tenth, the decimal becomes x.y

(1) That means y>=5, y = {5, 6, 7, 8, 9};
x = y - 1, x = {4, 5, 6, 7, 8} -----> x.yx = 4.54; 5.65; 6.76; 7.87; 8.98 Insufficient.

(2) Means x < 5, x = {1, 2, 3, 4} Insuficient.

(1) & (2) x = {1, 2, 3, 4}∩{4, 5, 6, 7, 8} = 4. Sufficient.

Senior Manager
Joined: 02 Apr 2014
Posts: 473
GMAT 1: 700 Q50 V34
Re: Let x and y be two distinct digits in the decimal x.yx, what is x?  [#permalink]

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03 Nov 2017, 11:38
Statement 1: When rounded to the nearest integer, the decimal becomes y
=> $$y >= 5$$ and $$y - x = 1$$
=> eg. $$6.76$$ => rounded to nearest integer => $$7$$
$$5.65$$ => rounded to nearest integer =>$$6$$
so not sufficient to get x

Statement 2: When rounded to the nearest tenth, the decimal becomes x.y

=> $$x < 5$$
=> eg. $$3.43$$ => rounded => $$3.4$$
eg $$2.32$$ => rounded => $$2.3$$
still insuff

Statement 1 + 2, => $$y>= 5 && y - x = 1$$ and $$x < 5$$, only combination possible is $$y = 5$$ and $$x = 4$$=> sufficient => Answer (C)
Re: Let x and y be two distinct digits in the decimal x.yx, what is x? &nbs [#permalink] 03 Nov 2017, 11:38
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