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A total of 22 men and 26 women were at a party, and the average
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20 Oct 2015, 03:06
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A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women? (A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33 Kudos for a correct solution.
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Re: A total of 22 men and 26 women were at a party, and the average
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20 Oct 2015, 06:18
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. One can use the weighted average method: \(\frac{Weight 1}{Weight 2} = \frac{Average2Average}{AverageAverage1}\) For or example: \(\frac{26}{22} = \frac{3835}{35Average1}\) Solving for Average1 you will get exactly 32.46154. Answer D.
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Re: A total of 22 men and 26 women were at a party, and the average
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20 Oct 2015, 03:43
Let Aw = average age of women Average = (Number of men X average age of men + Number of women X average age of women)/total number of people 35 * 48 = 22 * 38 + 26 * Aw =>1680 = 836 + 26 Aw => 26 Aw = 844 =>Aw = 32.5 Answer D Scale method  If number of men and women were equal , the average would have been at the center of the average age of the individual groups Average age of women = 32 as 35 will be equidistant from 32 and 38 (average age of men) At this point we can eliminate A , B and C But since , number of women are more , average age will be more than 32 Ratio of women to men = 26:22 = 13:11 If Aw= 32.5 Distance from the average 35 32.5 :3835 2.5 :3 5:6 which is rougly equal to inverse of 13:11 Answer D
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Re: A total of 22 men and 26 women were at a party, and the average
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20 Oct 2015, 07:09
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. You can also think of it like this on a scale method base: x(Average female)..........(35x)............Average(35)..........(3)............(38)Average male #26 (No. of females)..........................................................................#22 (No. of males) So again this shows that we have to groups which mixed together have an a weighted average of 35. The "weighs" in this example are the number of people. For men 22 and for woman 26. You can now equate the known weighs with the differences to average: \(\frac{26}{22}=\frac{3}{(35x)}\) Then solve for x to get x= 32.4615 Answer D.
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Re: A total of 22 men and 26 women were at a party, and the average
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20 Oct 2015, 07:40
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. 38*22 + W*26 = 35*(22+26) i.e. W = 844/26 = 32.46 = 32.5 Answer: option D
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A total of 22 men and 26 women were at a party, and the average
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Updated on: 06 Mar 2018, 10:49
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...There are 48 people in total. So, 22/48 = the proportion of womenAnd 26/48 = the proportion of menLet x = average age of the womenSo, plugging the information into the formula, we get: (22/48)(38) + (26/48)(x) = 35 Simplify: (11/24)(38) + (13/24)(x) = 35 Multiply both sides by 24 to get: (11)(38) + 13x = (35)(24) Simplify: 418 + 13x = 840 Rearrange: 13x = 422 Solve: x = 422/13 ≈ 32.5 Answer: D Cheers, Brent
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Originally posted by GMATPrepNow on 20 Oct 2015, 08:03.
Last edited by GMATPrepNow on 06 Mar 2018, 10:49, edited 1 time in total.



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Re: A total of 22 men and 26 women were at a party, and the average
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21 Oct 2015, 04:54
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. let average age of women be x then, we have \(22 * 38 + 26 * x = 48 * 35\) => \(x = 32.46\) Answer choice D



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Re: A total of 22 men and 26 women were at a party, and the average
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19 Mar 2016, 11:41
I followed a similar approach to the scale. Given that m:w is 11:13 and we know that the AVG(m) = 38 and AVG(m+w)=35. We already know the AVG(w) has to be less than 35 given the higher weighting to w. I ended up multiplying the (11/13) * 38. To simplify, I rounded to redo the formula as (11/13)*39 = 33. Therefore, the answer must be just under 33 or 32.5. Also, keep in mind the key word of "closest", which implies that you do not need an EXACT answer (no crazy math).



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Re: A total of 22 men and 26 women were at a party, and the average
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04 May 2016, 09:55
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. 1) Since there are 48 people (22 men and 26 women) and the average age of all of them is 35, the total ages of all the people at the party is 48(35). 2) Since there are 22 men and their average age is 38, the sum of all the men's ages is 22(38). 3) There are 26 women; letting their average age be x, the sum of all the women's ages is 26x. Since the sum of the ages of all 48 people must be equal to the sum of the ages of the 22 men plus the sum of the ages of the 26 women, we have 48(35) = 22(38) + 26x 1680 = 836 + 26x 26x = 844 x = 844/26 x = 32 12/26 ≈ 32.5 Answer: D
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A total of 22 men and 26 women were at a party, and the average
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04 May 2016, 10:23
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. Total age of men and women = 48*35 => 1,680 Total age of men is = 22*38 => 836 So, total age of women in = 1680  836 => 844 Average age of women is 844/26 => 32.46 Hence answer will be (D) 32.5
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Re: A total of 22 men and 26 women were at a party, and the average
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16 May 2016, 20:05
Here is the MGMAT Solution to it. Avg. age of men is +3 than the avg. age of the group. Now, 3(22)+w(26)=0....(Make this differential cancel out,hence equal to 0) 22=no. of men 26=no. of women 3=differential from mean. Hence w=2.5 Thus group mean (35)+Differential (2.5)=32.5 Hope its simple than all the long calculations.



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Re: A total of 22 men and 26 women were at a party, and the average
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11 Aug 2016, 06:42
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. I uesd the Std Deviation method : Ave of Man = 38 (which is 3835 = 3 more than the ave of Man & Women together) and No of man = 22 Therefore Deviation More than the Mean = 3 * 22 = 66 Also, we know that No of women = 26 Now, For any given set of numbers, Deviation More than the Mean is ALWAYS = Deviation Less than the Mean Therefore, each women can have a deviation of = 66/26 ~= 2.5 from the Average Value Therefore, Ave age of Women = 352.5 = 32.5 Kudos if u like the method....



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Re: A total of 22 men and 26 women were at a party, and the average
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09 Oct 2016, 16:02
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. It initially took mme ~2mins to solve this, but tried a couple of ways and think weighted avg would be fastest as lesser big numbers to deal with: [Womenavg: (w)]3538 \(\frac{26}{22} = \frac{3}{(35w)}\) \(w = 35  \frac{33}{13}\) 13 * 2 = 26; hence \(\frac{33}{13} = 2.x\) (I wont even bother getting the decimal) w = 35  2.x = 32.x (~32.5)
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Re: A total of 22 men and 26 women were at a party, and the average
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17 May 2019, 19:18
Hi there Could you explain the logic behind this ratio formula please? Thanks so much!! reto wrote: Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. One can use the weighted average method: \(\frac{Weight 1}{Weight 2} = \frac{Average2Average}{AverageAverage1}\) For or example: \(\frac{26}{22} = \frac{3835}{35Average1}\) Solving for Average1 you will get exactly 32.46154. Answer D. Posted from my mobile device



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Re: A total of 22 men and 26 women were at a party, and the average
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17 May 2019, 20:50
average age of man * number of men = summation of ages of men average age of woman * number of women = summation of ages of women
summation of ages of men + summation of ages of women = summation of ages of men and women
Thus, (38*22) + (average age of woman*26) = 35*(22+26)
simplifying, average age of woman = {[35*(22+26)](38*22)}/26 = a little greater than 32 => 32.5
Answer: D



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Re: A total of 22 men and 26 women were at a party, and the average
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11 Oct 2019, 03:46
GMATPrepNow wrote: Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. Weighted average of groups combined = (group A proportion)(group A average) + (group B proportion)(group B average) + (group C proportion)(group C average) + ...There are 48 people in total. So, 22/48 = the proportion of womenAnd 26/48 = the proportion of menLet x = average age of the womenSo, plugging the information into the formula, we get: (22/48)(38) + (26/48)(x) = 35 Simplify: (11/24)(38) + (13/24)(x) = 35 Multiply both sides by 24 to get: (11)(38) + 13x = (35)(24) Simplify: 418 + 13x = 840 Rearrange: 13x = 422 Solve: x = 422/13 ≈ 32.5 Answer: D Cheers, Brent How can we assume that 35 is the weighted average and not a simple avg of 48 people in total ?



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Re: A total of 22 men and 26 women were at a party, and the average
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19 Oct 2019, 08:21
It is given that the exact age of men is 38, whereas the average age of man and women is 35. That means, every man sacrifice 3 years to set the given average i.e 35. Mathematically, from the age of 22 men, we get 66 years to be added up to the age of woman. As there are 26 woman, each one gets 2.7/13 years. Thus the age of a woman is 35 2.7/13 = 32.50 years.



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Re: A total of 22 men and 26 women were at a party, and the average
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21 Oct 2019, 15:28
mimajit wrote: How can we assume that 35 is the weighted average and not a simple avg of 48 people in total ? The average = 35 = weighted average They are the same thing. The "weight" here is dictated by the number of women compared to the number of men. Cheers, Brent
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Re: A total of 22 men and 26 women were at a party, and the average
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21 Oct 2019, 18:13
average age 35 22 man adds extra 22*3=66 yrs. 26 women must neutralize 66 years. so (3532.5=2.5) 2.5*26=65 (closest to 66) so 32.5 is the answer



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Re: A total of 22 men and 26 women were at a party, and the average
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29 Oct 2019, 12:26
Bunuel wrote: A total of 22 men and 26 women were at a party, and the average (arithmetic mean) age of all of the adults at the party was exactly 35 years. If the average age of the men was exactly 38 years, which of the following was closest to the average age, in years, of the women?
(A) 31 (B) 31.5 (C) 32 (D) 32.5 (E) 33
Kudos for a correct solution. I solved it in 49 seconds and here is the approach. Average Age = 35. 22 people have contributed = +3 each. Which means we are 66 above the average. 26 people have to reduce the total of their age by 66 to keep the average intact at 35. 66/26=33/13=2.53=2.5 So each goes 2.5 below the average which is 35. Hence 32.5 Answer D
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Re: A total of 22 men and 26 women were at a party, and the average
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