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PS (600 Level)

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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PS (600 Level)

by Pranavb1302 » Thu Oct 08, 2020 9:52 am
If R, S and T are numbers, is R=60?

(1) The average (arithmetic mean) of R, S and T is 20.
(2) S=T=0

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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Re: PS (600 Level)

by mapadvantageprep » Sun Mar 03, 2024 12:19 am
Statement (1): The average (arithmetic mean) of R, S, and T is 20.

The average of three numbers being 20 means that the sum of the numbers is 60 because the average is the sum divided by the number of items. So,
R+S+T=60. This statement alone does not tell us whether
R=60; the value of R depends on S and T. Therefore, Statement (1) alone is not sufficient.

Statement (2):
S=T=0
With
S=0 and
T=0, this directly impacts the sum
R+S+T. If both S and T are zero, then the entire sum of the three numbers would just be
R. However, this statement alone does not provide information about the total sum or the specific value of R, nor does it directly connect to the condition
R=60 without additional context, such as their sum or average. Yet, by common interpretation but not strict mathematics here, this still doesn't confirm
R=60 directly; it merely informs us of the values of S and T.
However, there's an important note: if you're familiar with algebra, you might realize that if the other variables (intended to add with R to reach a sum) are zero, and if we were expecting a sum (like from the context of statement 1, even though we shouldn't combine until we evaluate both), this could mislead. But per strict GMAT logic or usual algebra, without an initial sum condition here, it's not directly about
R being 60 alone from this statement.

Combining Statements (1) and (2):

If the average of
R,S, and T is 20, then
R+S+T=60. And if
S=0 and
T=0, then substituting these into the sum from Statement (1),
R+0+0=60, which means
R=60.

When we combine the statements, they are sufficient together to conclude that
R=60. Neither statement alone is sufficient to conclude that
R=60, but together, they provide enough information.

Thus, the correct answer is C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.


Bernard Baah
MS '05, Stanford
GMAT and GRE Instructor
MapAdvantage Prep
https://mapadvantagegmat.com
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Re: PS (600 Level)

by marybrand » Tue May 28, 2024 6:05 pm
Pranavb1302 wrote: ↑
Thu Oct 08, 2020 9:52 am
 If R, S and T are numbers, is R=60?

(1) The average (arithmetic mean) of R, S and T is 20.
(2) S=T=0

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
To determine whether R = 60, we need to analyze the given statements one by one and then together.
Statement (1): The average (arithmetic mean) of R, S , and T is 20.
The arithmetic mean of R, S, and T being 20 means:
(R + T + S)/3 = 20
Multiplying both sides by 3 gives:
R + S + T = 60
From this equation, we know the sum of \( R, S \), and \( T\) is 60. However, the problem asks whether \( R = 60 \). \( R \) is not explicitly defined in the problem even though it appears similar to the result we derived ( R+ S + T = 60 ). However we cannot assume R = R + S + T . If R = R + S + T , then from this statement alone, we can conclude:
R = 60 BUT we do not know that for sure.
Hence, statement (1) alone is insufficient.

Statement (2): S = T = 0
Given S = 0 and T = 0, we substitute these into the assumed formula R = R + S + T:
R = R + 0 + 0 = R
However, this does not provide us with any information about the value of R, and thus we cannot determine R uniquely. Therefore, statement (2) alone is not sufficient to determine whether R = 60.

Combining both statements:
From statement (2), S = 0 and T = 0 :
so R = R
From statement (1), R+ S +T = 60 . Substituting S = 0 and T = 0 :
R+ 0 + 0 = 60 => R = 60
Thus, combining both statements, we get R = 60.
Therefore, each statement alone does not provide enough information, but both statements together are sufficient to determine that R = 60.
Final Answer: C
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