Data Sufficiency

sitsmegain wrote:Hello ALL,
As per my solving, we need both (1)and (2) to solve this problem, but i want to be sure that my understanding is right. So what will be the correct answer and how?

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A group of men and women competed in a marathon. Before the competition, each competitor was weighed and the average weight of the female competitors was found to be 120 lbs, while the average weight of the men was found to be 150 lbs. What was the average weight of all of the competitors?

(1) 100 men competed in the marathon.
(2) There were twice as many men as women competing in the marathon.
*******************************************************************

Weighted average questions typically involve 3 key pieces of information:

Fact 1: the average/percentage of each element to be combined
Fact 2: the ratio of the elements when they are combined
Fact 3: the resulting average/percentage when the elements are combined

If we are given Fact 1 and Fact 2, we can determine Fact 3.
If we are given Fact 1 and Fact 3, we can determine Fact 2.

The DS question above asks for Fact 3: the resulting average.
The question stem provides Fact 1: the average of each of the elements to be combined (120 for the women, 150 for the men).
Thus, we need Fact 2: the ratio of men to women.

Statement 2 provides the needed ratio: There were twice as many men as women.
Sufficient. No math is needed.

Recognizing the basic construction of weighted average problems makes this a very quick DS question to answer.

GMATGuruNY wrote:

sitsmegain wrote:Hello ALL,
As per my solving, we need both (1)and (2) to solve this problem, but i want to be sure that my understanding is right. So what will be the correct answer and how?

****************************************************************
A group of men and women competed in a marathon. Before the competition, each competitor was weighed and the average weight of the female competitors was found to be 120 lbs, while the average weight of the men was found to be 150 lbs. What was the average weight of all of the competitors?

(1) 100 men competed in the marathon.
(2) There were twice as many men as women competing in the marathon.
*******************************************************************

Weighted average questions typically involve 3 key pieces of information:

-- the average/percentage of each element to be combined
-- the ratio of the elements when they are combined
-- the resulting average/percentage when the elements are combined

If we have any 2 of these 3 pieces of information, we can solve for the third.

In DS question above, we're being asked for the resulting average, and we're given the average of each of the elements to be combined (120 for the women, 150 for the men). Statement 2 provides the missing piece (the ratio of the elements), so it's sufficient. No math is needed.

Recognizing the basic construction of weighted average problems makes this a very quick DS question to answer.

GMATGuru,

Do you have a sample question using percentages? I tried to plug in my own numbers to practice one using the above question as a base, but it didn't turn out very pretty...

Thanks!

aleph777 wrote:

GMATGuruNY wrote:

sitsmegain wrote:Hello ALL,
As per my solving, we need both (1)and (2) to solve this problem, but i want to be sure that my understanding is right. So what will be the correct answer and how?

****************************************************************
A group of men and women competed in a marathon. Before the competition, each competitor was weighed and the average weight of the female competitors was found to be 120 lbs, while the average weight of the men was found to be 150 lbs. What was the average weight of all of the competitors?

(1) 100 men competed in the marathon.
(2) There were twice as many men as women competing in the marathon.
*******************************************************************

Weighted average questions typically involve 3 key pieces of information:

-- the average/percentage of each element to be combined
-- the ratio of the elements when they are combined
-- the resulting average/percentage when the elements are combined

If we have any 2 of these 3 pieces of information, we can solve for the third.

In DS question above, we're being asked for the resulting average, and we're given the average of each of the elements to be combined (120 for the women, 150 for the men). Statement 2 provides the missing piece (the ratio of the elements), so it's sufficient. No math is needed.

Recognizing the basic construction of weighted average problems makes this a very quick DS question to answer.

GMATGuru,

Do you have a sample question using percentages? I tried to plug in my own numbers to practice one using the above question as a base, but it didn't turn out very pretty...

Thanks!

Here are some weighted average questions to which I've posted solutions:

https://www.beatthegmat.com/percents-and ... 67622.html

https://www.beatthegmat.com/probability- ... 67339.html

https://www.beatthegmat.com/weighted-ave ... 71702.html

https://www.beatthegmat.com/ratios-question-t71528.html

https://www.beatthegmat.com/seed-mixture-t21603.html

https://www.beatthegmat.com/allegation-t69552.html

https://www.beatthegmat.com/the-average- ... 70430.html

https://www.beatthegmat.com/percentage-p ... 70078.html

https://www.beatthegmat.com/alloy-t68698.html

Option 2 is sufficient to annswer the question.

+1 for B. Only the second statement is required.

i didn't see an OA anywhere..it has be 'B'

Without solving i thought its C, Didnt realize that 2 statement can be transformed into a algebric equation ...Which can be solved ..
B

(gmatguruNY).i think the answer should be C as we can have any number of women and twice the number of them as men for example if we take the number of women to be then 2x will be the number of men.we can take any numbers for them example:2 women then 4 men,8 women then 16 men

B..

Option (2) is sufficient to answer the question.

I dont want to explain my answer ..if any body really wants it ..i can explain it..
according to me the correct anser is 140 lbs...

and we need boyh of the option 1 and 2 to solve this answer.

Bravo Mitch,

You brought always a new angle of solving Qs.. You should really rename your BTGid to PlugMaster .. amazing ..

GMATGuruNY wrote:

sitsmegain wrote:Hello ALL,
As per my solving, we need both (1)and (2) to solve this problem, but i want to be sure that my understanding is right. So what will be the correct answer and how?

****************************************************************
A group of men and women competed in a marathon. Before the competition, each competitor was weighed and the average weight of the female competitors was found to be 120 lbs, while the average weight of the men was found to be 150 lbs. What was the average weight of all of the competitors?

(1) 100 men competed in the marathon.
(2) There were twice as many men as women competing in the marathon.
*******************************************************************

When a DS question asks for a specific amount -- in this case, the average weight of the whole group -- a good way to check whether a statement is sufficient:

Plug in TWICE. If the value being sought stays the same, the statement is sufficient. If the value being sought changes, the statement is insufficient.

Looking at statement 2: twice as many men as women
Plug in M=2, W=1
Total weight of M = 2*150 = 300.
Total weight of W = 1*120 = 120.
Average of the whole group = 420/3 = 140.

Plug in M=4, W=2.
Total weight of M = 4*150 = 600.
Total weight of W = 2*120 = 240.
Average of the whole group = 840/6 = 140.

Since in each case the average weight of the whole group is 140, the statement is sufficient.

The correct answer is B.

DS questions become much clearer when we plug in actual values.

I chose B because the built in 2:1 ratio is scalable.

You scored a 790? You sir, are not human.

GMATGuruNY wrote:

sitsmegain wrote:Hello ALL,
As per my solving, we need both (1)and (2) to solve this problem, but i want to be sure that my understanding is right. So what will be the correct answer and how?

****************************************************************
A group of men and women competed in a marathon. Before the competition, each competitor was weighed and the average weight of the female competitors was found to be 120 lbs, while the average weight of the men was found to be 150 lbs. What was the average weight of all of the competitors?

(1) 100 men competed in the marathon.
(2) There were twice as many men as women competing in the marathon.
*******************************************************************

When a DS question asks for a specific amount -- in this case, the average weight of the whole group -- a good way to check whether a statement is sufficient:

Plug in TWICE. If the value being sought stays the same, the statement is sufficient. If the value being sought changes, the statement is insufficient.

Looking at statement 2: twice as many men as women
Plug in M=2, W=1
Total weight of M = 2*150 = 300.
Total weight of W = 1*120 = 120.
Average of the whole group = 420/3 = 140.

Plug in M=4, W=2.
Total weight of M = 4*150 = 600.
Total weight of W = 2*120 = 240.
Average of the whole group = 840/6 = 140.

Since in each case the average weight of the whole group is 140, the statement is sufficient.

The correct answer is B.

DS questions become much clearer when we plug in actual values.

I just picked numbers to solve this and found that answer choice B was the correct answer. For B, you can choose 5 women, 10 men or 3 women and 6 men and you come to the same number. I just made men weight 15 pounds and women weigh 12 pounds. Much more easier in my opinion!

Answer choice A tells us nothing about women and if you choose numbers, you get different numbers.

Amazing question.