During the first 3 weeks of a 10-week diet program

Question

During the first 3 weeks of a 10-week diet program, Bob lost an average of 5 pounds per week. During the final 7 weeks of the program, he lost an average of 2 pounds per week. If he lost the same amount of weight during the first 3 weeks of the program as during the last 3 weeks of the program, how much weight had Bob lost after the seventh week of the diet program ?
(A) 15
(B)12
(C)14
(D)16
(E)13

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The official answer says :
His total loss during 1st 3 weeks 15 pounds. This is also the amount of weight he lost during the last three weeks. Thus, his total weight loss during all but the fourth through seventh weeks was 30 pounds.
Given that he lost 29 pounds altogether during the 10 weeks [(3*5)+(7*2)], he must have gained 1 pound during the fourth through seventh week. Accordingly, he had lost 14 pounds (-15+1) after the first seven weeks. so the Answer is (B) . :-D

blueseas · Answer

in first 3 weeks lost =  5+5+5 =15 
in last 7 weeks lost =  2+2+2+2+2+2+2 = 14 
in last 3 weeks lost = same as first 3 weeks =  15

therefore lost in  FIRST 7 weeks  = lost in first 3 + lost in last 7 - lost in last 3 =  15 + 14 - 15 =14 
hence C

Asifpirlo · Answer

but the question is " how much weight had Bob lost after the seventh week " not lost in 1st 7 weeks

Asifpirlo · Answer

The official answer says :
His total loss during 1st 3 weeks 15 pounds. This is also the amount of weight he lost during the last three weeks. Thus, his total weight loss during all but the fourth through seventh weeks was 30 pounds.
Given that he lost 29 pounds altogether during the 10 weeks [(3*5)+(7*2)], he must have gained 1 pound during the fourth through seventh week. Accordingly, he had lost 14 pounds (-15+1) after the first seven weeks. so the Answer is (C) . :-D

blueseas · Answer

its the same thing what i meant..

Transcendentalist · Answer

Answer is B? :roll:

It should be C Asif whats the source of these questions?

Asifpirlo · Answer

where did you find answer is B....!! obviously answer is (C).. i mentioned it. :-D

hmmmm. typing error. but was correct in the option menu.. Source is Arco math book. www.arcotestprep.com

jlgdr · Answer

Actually the question is not clear. It should say how much weight did the fatty lose by the end of week 7 or something along those lines

Not GMAT quality questions

Cheers

PareshGmat · Answer

Answer = C = 14

First 3 weeks, weight lost = 15 pounds

Next 4 weeks, he gained weight = 1 pound

SO total weight lost after 7 weeks = 15-1 = 14

dransa · Answer

I think the question asks that how much of weight is lost from the start of the diet program to end of the seventh week. It the question were asking about the wight lost in the last 3 weeks, then the question would have been "how much of weight is lost after the 7th week till the end of the program? / how much of weight is lost between the 8th week and the end of the program ".

Rishm · Answer

Agreed, but his name is bob and not fatty.

egmat · Answer

Let's break this problem into clear pieces.

Step 1:  Find total weight lost in the FIRST  3  weeks (weeks  1 - 3 ).
Average =  5  pounds/week ×  3  weeks =  15  pounds.

Step 2:  Find total weight lost in the LAST  7  weeks (weeks  4 - 10 ).
Average =  2  pounds/week ×  7  weeks =  14  pounds.

So total weight lost over all  10  weeks =  15  +  14  =  29  pounds.

Step 3:  Now use the special condition — he lost the SAME amount in the first  3  weeks as in the last  3  weeks.
First  3  weeks (weeks  1 - 3 ) =  15  pounds.
So the last  3  weeks (weeks  8 - 10 ) =  15  pounds too.

Step 4:  The question asks how much weight Bob lost after  7  weeks (meaning by the end of week  7 ).

Think of it this way:
Weight lost in weeks  1  through  7  + Weight lost in weeks  8  through  10  = Total weight lost
Weight lost in weeks  1  through  7  +  15  =  29 
Weight lost in weeks  1  through  7  =  29  -  15  =  14  pounds.

Answer: C (14)

The trick here  is recognizing that the last  3  weeks (weeks  8 - 10 ) are part of the last  7  weeks (weeks  4 - 10 ), so their weight loss of  15  pounds must come out of that  14 -pound bucket for weeks  4 - 10 . This means Bob actually GAINED  1  pound during weeks  4 - 7 , and then lost heavily in weeks  8 - 10 . But for the total through week  7 , it's simply  29  -  15  =  14 .

During the first 3 weeks of a 10-week diet program

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