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If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths

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If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths

by BTGModeratorVI » Thu Jun 18, 2020 5:45 am

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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

Answer: D
Source: Official guide
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Re: If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths

by Jay@ManhattanReview » Fri Jun 19, 2020 2:11 am
BTGModeratorVI wrote: ↑
Thu Jun 18, 2020 5:45 am
 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

Answer: D
Source: Official guide
So, we have to make the fraction (0.1X)/(0.02Y) greatest.

=> Make the numerator 0.1X greatest and 0.02Y smallest.

The greatest nonzero digit is 9, so X = 9 and the smallest nonzero digit is 1. SO, Y =1

=> Greatest Value of (0.1X)/(0.02Y) = (0.19)/(0.021) = 190/21 = ~9

Correct answer: D

Hope this helps!

-Jay
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Re: If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths

by Brent@GMATPrepNow » Fri Jun 19, 2020 5:31 am
BTGModeratorVI wrote: ↑
Thu Jun 18, 2020 5:45 am
 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

Answer: D
Source: Official guide
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
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Re: If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths

by gentvenus » Fri Jun 19, 2020 9:51 am
To max a fraction, we must max the numerator (0.1X) and min the denominator (0.02Y)
The numerator is max when X = 9
The denominator is min when Y = 1
So, answer must be closest to 9/1 = 9
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Re: If X is the hundredths digit in the decimal 0.1X and if Y is the thousandths

by Scott@TargetTestPrep » Sun Jun 21, 2020 4:54 am
BTGModeratorVI wrote: ↑
Thu Jun 18, 2020 5:45 am
 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

Answer: D
Source: Official guide
Solution:

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


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