For a cause, 30 people donated $10, $20, or $30.

Question

For a cause, 30 people donated $10, $20, or $30. What was the average (arithmetic mean) amount contributed per person?

(1) The number of people who donated $10 was the same as the number of people who donated $30.

(2) The number of people who donated $10 was the same as the number of people who donated $20.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statement (1) and (2) TOGETHER are NOT sufficient

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Official Answer

A

Bunuel · Answer

You posted this in the PS forum, so I’ve moved it to the correct section — the DS forum. Please make sure to post questions in the appropriate forum moving forward. Thank you.

RakshitaR · Answer

why can it not be D,

(1)
( 10a + 20 b + 30 c )/30 = average mean
( 10a + 20 (30-2a) + 30 a ) / 30
20*30/30
= 20
sufficient
(2)
( 10a+20a+30(30-a))/30
=30*30/30
= 30
sufficient

Kunal.lost · Answer

There's a calculation mistake in the second one.

It should be 10a+ 20a + 30 ( 30-2a )

Solve this ahead and you'll know you can't cancel 'a' out like you did in the first one.

So (2) is insufficient.

Answer is (A).

ReetArora · Answer

Should'nt C be the answer...together they both are sufficient. How 1st alone is sufficient?

Kunal.lost · Answer

So there's a certain sequence followed while approaching Data Sufficiency questions.

You'll find videos explaining it on YouTube. Look for any basic DS video from GMATClub or GMATNinja on YouTube.

Adit_ · Answer

These kind of problems are the base for advanced weighted averages problems which IMO are the hardest kind in DS questions.
This IMO can pretty much be remembered in the sense that whenever we have such a problem the first thing we need to do is solve and see if there is a common factor before jumping to any conclusion.

1st statement is sufficient as it gives us 20 as the answer.
Even logically speaking this can come in handy:
When we have 10,20,30:
x,y,z being the number of items of each of the kind then,
if x is greatest value is closer to 10, y is greatest then closer to 20 and so on,
We somehow also have 20 as the average between 10,30.
When both 10 and 30 become equal in other words 10+30/2 = 20
Whether it is 10*2+30*2/4 or any multiple it always leads us to 20 only.
So equal items of 10 and 30 gives us 20 because its the midpoint.
Remaining is 20 and any number of items of 20 will always give 20 anyway so we have an average of a amounts of 20 and b amounts of 20 which is obviously 20 only.

Answer:  Option A

For a cause, 30 people donated $10, $20, or $30.

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GMAT Data Sufficiency (DS) Questions

For a cause, 30 people donated $10, $20, or $30.

Prep Toolkit

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