OG If x is the hundredths digit

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AbeNeedsAnswers: Master | Next Rank: 500 Posts; Posts: 394; Joined: Sun Jul 02, 2017 10:59 amFollowed by: 5 members; Thanked: 1 times

by AbeNeedsAnswers » Fri Aug 18, 2017 5:52 pm

If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths digit in the decimal 0.02Y ,where X and Y are nonzero digits,which of the following is closest to the greatest possible value of 0.1X/0.02Y ?

A. 4
B. 5
C. 6
D. 9
E. 10

D

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Source: Beat The GMAT — Problem Solving | Fri Aug 18, 2017 5:52 pm

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by [email protected] » Sat Aug 19, 2017 9:46 am

Hi AbeNeedsAnswers,

We're told that X is the hundredths digit in the decimal 0.1X and if Y is the thousandths digit in the decimal 0.02Y and that X and Y are NON-ZERO digits. We're asked which of the following is closest to the GREATEST possible value of 0.1X/0.02Y

To make the value of this positive fraction as large as possible, we need to make the numerator as large as possible AND make the denominator as small as possible... so we should make X = 9 and Y = 1.

.19/.021

To 'clean up' this fraction, let's multiply both the numerator and denominator by 1000....

190/21

At this point, you might find it useful to compare 'multiples' of 21...
(21)(9) = 189
(21)(10) = 210

189 is considerably closer to 190 than 210 is, so that fraction is closest to 9.

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Wed Aug 23, 2017 1:00 pm

AbeNeedsAnswers wrote:If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths digit in the decimal 0.02Y ,where X and Y are nonzero digits,which of the following is closest to the greatest possible value of 0.1X/0.02Y ?

A. 4
B. 5
C. 6
D. 9
E. 10

D

To MAXIMIZE the value of 0.1X/0.02Y, we must MAXIMIZE the numerator (0.1X) and MINIMIZE the denominator (0.02Y)

So, the numerator is maximized when X = 9. So, the numerator is 0.19
The denominator is minimized when Y = 1. So, the denominator is 0.021

So, we must determine the value of 0.19/0.021

IMPORTANT: We need not calculate the value of 0.19/0.021
Instead, just recognize that 0.19/0.02 = 9.5, which is halfway between 9 and 10
Since 0.021 is a bit bigger than 0.02, we know that 0.19/0.021 is a bit LESS THAN 9.5
So, 0.19/0.021 must be closest to 9

Answer: D

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8139; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

Re: OG If x is the hundredths digit

by Scott@TargetTestPrep » Sun Feb 16, 2020 7:16 am

AbeNeedsAnswers wrote: ↑
Fri Aug 18, 2017 5:52 pm
If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths digit in the decimal 0.02Y ,where X and Y are nonzero digits,which of the following is closest to the greatest possible value of 0.1X/0.02Y ?

A. 4
B. 5
C. 6
D. 9
E. 10

D

We are given two decimals:

0.1X and 0.02Y

To make 0.1X the greatest, we can let X = 9 and we have:

0.19

To make 0.02Y the smallest, we can make Y = 1 (since Y = 0 is not allowed) and we have:

0.021

Thus:

0.19/0.021 = 190/21 = 9 1/21

So, the greatest possible value is about 9.

Answer: D

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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