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If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

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If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

by BTGModeratorVI » Sat Aug 08, 2020 7:13 am

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If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x

Answer: A
Source: Official guide
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Source: — Data Sufficiency |

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Re: If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

by Brent@GMATPrepNow » Sat Aug 08, 2020 12:19 pm

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BTGModeratorVI wrote: ↑
Sat Aug 08, 2020 7:13 am
 If x is a positive number less than 10, is z greater than the average (arithmetic mean) of x and 10?

(1) On the number line, z is closer to 10 than it is to x.
(2) z = 5x

Answer: A
Source: Official guide
Target question: Is z greater than the mean of x and 10?

Statement 1: On the number line, z is closer to 10 than it is to x.
IMPORTANT: On the number line, the mean of two numbers will lie at the midpoint between those two numbers.
So, the mean of x and 10 will lie halfway between x and 10.
So, if z is closer to 10 than it is to x, then z must lie to the right of the midpoint between x and 10.
This means that z must be greater than the mean of x and 10
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: z = 5x
There are several pairs of numbers that meet this condition. Here are two:
Case a: x=1, z=5, in which case z is less than the mean of x and 10 (mean = 5.5)
Case b: x=4, z=20, in which case z is greater than the mean of x and 10 (mean = 7)
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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