If S is a set of distinct positive multiples of 5, what is the smalles

Question

If S is a set of distinct positive multiples of 5, what is the smallest element of S?

(1) The mean of S and the median of S both equal 20.
(2) The largest element of S is 40.

D3N0 · Answer

Ans: NOT A Not B Not D ------------- C or E not sure
1) (20) (5,20,35) (10,20,30)(15,25)  
2) (40) (5,40) (10,40) (20,40)

I know statement A and B alone are not sufficient
but there are so many possibilities with even number of elements and odd number of elements in set and calculating median and avg for all are too time consuming.
What is the trick here.. ? How to solve this in 2 min?

VenoMfTw · Answer

IMO: C

St 1: The mean of S and the median of S both equal 20.

Different sets are possible - {20} , {15,20,25}, {10,15,20,25,30}, {5,10,15,20,25,30,35}
Hence Not suff

St 2: The largest element of S is 40.

Different Sets are possible - {40} , {10,40} .....

Combined: The mean of S and the median of S both equal 20. & largest element of S is 40

Only one possible combination : {5, 10, 20, 25, 40}.

hb4100 · Answer

VenoMfTw

Agree with everything except the final sentence. What if 0(which is also a multiple of 5) is considered. Then we have another set possible:{0,10,20,30,40},{0,15,20,25,40}. There are still at least two possible answers.

VenoMfTw · Answer

hb4100 
0 is not a positive integer. In question stem it is stated "positive integers".
Hence 0 is not possible.

odd_major · Answer

Bunuel  I believe that since the mean and the median both are 20, the sequence should be an AP.

These are the APs , I came up with based on the infor from S1 & S2 :

0, 5, 10, 15, || 20 || , 25, 30 , 35 , 40

0, 10, ||20||, 39, 40

0, ||20||, 40

However, in all these cases the smallest element is zero , which is not allowed per the question.

So , I choose 4 as the common difference :

0, 4, 8, 12, 16, ||20||, 24, 28, 32, 36, 40

In either case the smallest number is zero. How to resolve this issue?

Bunuel · Answer

Several points:

1. In an evenly spaced set (arithmetic progression), the median is equal to the mean, although the reverse isn't necessarily true. For example, consider the set {-1, 1, 2, 3, 5} where the median and mean are both 2, yet the set is not evenly spaced.

2. The question says that the set consists of distinct  positive  multiples of 5, thus the set cannot contain 0

3. The question says that the set consists of distinct positive  multiples of 5 , thus the set cannot contain 4, 8, 12, 16, 24, 28, 32, 36, or 39.

4. Pure algebraic questions are no longer a part of the  DS syllabus  of the GMAT.

DS questions in GMAT Focus encompass various types of word problems, such as:

Word Problems 
 Work Problems 
 Distance Problems 
 Mixture Problems 
 Percent and Interest Problems 
 Overlapping Sets Problems 
 Statistics Problems 
 Combination and Probability Problems

While these questions may involve or necessitate knowledge of algebra, arithmetic, inequalities, etc., they will always be presented in the form of word problems. You won’t encounter pure "algebra" questions like, "Is x > y?" or "A positive integer n has two prime factors..."

Check  GMAT Syllabus for Focus Edition

You can also visit the  Data Sufficiency forum  and filter questions by  OG 2024-2025, GMAT Prep (Focus), and Data Insights Review 2024-2025 sources  to see the types of questions currently tested on the GMAT.

So, you can ignore this question.

Hope it helps.

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If S is a set of distinct positive multiples of 5, what is the smalles

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If S is a set of distinct positive multiples of 5, what is the smalles

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