Digit Inequality

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rahul26: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sun Jul 13, 2008 9:16 am

by rahul26 » Mon Mar 30, 2009 10:42 am

7.5xy9
What digit does x represent if each of x and y and are single digits in the above decimal?
1. If the decimal is rounded to the nearest hundredth, the result is 7.55.
2. If the decimal is rounded to the nearest tenth, the result is 7.5.
(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.

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Source: Beat The GMAT — Data Sufficiency | Mon Mar 30, 2009 10:42 am

mavesum: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Sun Aug 31, 2008 11:20 pm

by mavesum » Mon Mar 30, 2009 11:09 am

IMO C

7.5xy9

S1 : If the decimal is rounded to the nearest hundredth, the result is 7.55.

that means x could be 5 and y could be (0-4)

7.5 5 (0-4)9

or

x could be 4 and y could be (5-9 )

7.5 4 (5-9)9

that is insufficient

S2 : If the decimal is rounded to the nearest tenth, the result is 7.5

x could be (0-4)

7.5 (0-4) y

insufficent

combining S1 and S2

tenth and hundreth digits are 5 , the only solution

7.5 4 (5-9)

thus x = 4

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rs2010: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jul 04, 2008 4:14 pmFollowed by: 1 member; Thanked: 14 times; GMAT Score:760

by rs2010 » Mon Mar 30, 2009 11:15 am

B gives 7.5 so X is less than 5
A gives 7.55 ie
x=5 if y <5--I
x=4 if y>5--II

Combining both we will get I

So C

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rahul26: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Sun Jul 13, 2008 9:16 am

by rahul26 » Mon Mar 30, 2009 11:37 am

hemantsood wrote:B gives 7.5 so X is less than 5
A gives 7.55 ie
x=5 if y <5--I
x=4 if y>5--II

Combining both we will get I

So C

My doubt is on this statement i.e x=4 if y>5--II
why we take x=4 , it can be 3,2 etc also.
Like if number is 7.5269

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rs2010: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jul 04, 2008 4:14 pmFollowed by: 1 member; Thanked: 14 times; GMAT Score:760

by rs2010 » Mon Mar 30, 2009 12:04 pm

rahul26 wrote:
hemantsood wrote:B gives 7.5 so X is less than 5
A gives 7.55 ie
x=5 if y <5--I
x=4 if y>5--II

Combining both we will get I

So C
My doubt is on this statement i.e x=4 if y>5--II
why we take x=4 , it can be 3,2 etc also.
Like if number is 7.5269

7.5269 will give, when rounded to hundreths digit, 7.53.

And in my explanation above i wanted to mention II by mistake I mentioned I

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