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What is the hundredths digit of th decimal Z?

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by BTGmoderatorDC » Thu Aug 02, 2018 5:39 pm

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Difficulty—

What is the hundredths digit of th decimal Z?

(1) The tenths digit of 100z is 2
(2) The units digit of 1,000z is 2

OA E

Source: GMAT Prep
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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Aug 02, 2018 7:44 pm
BTGmoderatorDC wrote:What is the hundredths digit of the decimal Z?

(1) The tenths digit of 100z is 2
(2) The units digit of 1,000z is 2
Statement 1:
100z = 0.2, 1.2, 2.2...
Dividing every value by 100, we get the following options for z:
z = 0.002, 0.012, 0.022...
Since the hundredth digit of z can be different values, INSUFFICIENT.

Every value in the blue list above also satisfies Statement 2.
Thus -- even when the statements are combined -- the hundredth digit of z can be different values.

The correct answer is E.
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by Brent@GMATPrepNow » Fri Aug 03, 2018 6:02 am
BTGmoderatorDC wrote:What is the hundredths digit of th decimal Z?

(1) The tenths digit of 100z is 2
(2) The units digit of 1,000z is 2

OA E

Source: GMAT Prep
Target question: What is the hundredths digit of the decimal z?

Statement 1: The tenths digit of 100z is 2
Notice what happens when we take a decimal like 0.123456 and multiply it by 100.
We get 12.345 (the tenths digit is 3)
In the original decimal, the 3 was in the thousandths place.
So, statement 1 tells us that the THOUSANDTHS digit of z is 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The unit digit of 1000z is 2
Notice what happens when we take a decimal like 0.123456 and multiply it by 1000.
We get 123.45 (the units digit is 3)
In the original decimal, the 3 was in the thousandths place.
So, statement 2 tells us that the THOUSANDTHS digit of z is 3
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

NOTE: Since statements 1 and 2 BOTH tell us the same thing (i.e., the THOUSANDTHS digit of z is 3), the combined statements are NOT SUFFICIENT

Answer: E

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Brent
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