Problem from Gurome blog- Doubt

Expert replies

rahulvsd: Master | Next Rank: 500 Posts; Posts: 184; Joined: Tue Sep 07, 2010 9:43 amFollowed by: 1 member; Thanked: 6 times

by rahulvsd » Wed Aug 24, 2011 7:54 pm

The length of an original steel bar is 7.3 meters. A 2.4 meters steel bar, a 2.1 meters steel bar, and a 1.5 meter steel bar are needed for a steel frame. If we want to build 100 steel frames, how many original steel bars at least do we need?

(A) 83

(B) 84

(C) 92

(D) 96

(E) 100

Hi I read this problem at the gurome blog. I have a doubt, the question says the total length of steel frame will be 6m, therefore for 100 steel frames it will be 600. So when we divide 600/7.3 we get 82.something which can be approximated to 83. However the answer given is 84.

Experts please help.[/spoiler]

Source: Beat The GMAT — Problem Solving | Wed Aug 24, 2011 7:54 pm

navami: Legendary Member; Posts: 540; Joined: Sat Dec 20, 2008 7:24 pmFollowed by: 6 members; Thanked: 37 times

by navami » Thu Aug 25, 2011 1:56 am

for 100 steel frames we need..
2.4 m bar = 100 nos
2.1 m bar = 100 nos
1.5 m bar = 100 nos

lets cut 3 pieces from 7.3 meters bar (each 2.4 meters long) .so ween need 100/3 = 33.33 ->7.3 m long steel bar. means 34 numbers 7.3 m steel bar.

---------|----------|----------|---
<---2.4-> <---2.4-> <---2.4-> <-.1->

and now if we cutout 2 pieces of 2.1m and 2 pieces of 1.5 meter long bars from 7.3 m long bar we need 50, 7.3 m long bars to cut out 100 pieces each.

------|------|---|---|--
<-2.1-><-2.1-><-1.5-><1.5>

so we need 50 + 34 = 84 bars.

This time no looking back!!!
Navami

gmatboost: Master | Next Rank: 500 Posts; Posts: 312; Joined: Tue Aug 02, 2011 3:16 pmFollowed by: 33 members; Location: New York City; Thanked: 130 times; GMAT Score:780

by gmatboost » Thu Aug 25, 2011 10:09 pm

rahulvsd,

You cannot divide 600 by 7.3 because that assumes that every piece of every bar is being used to build the frames.

However, it appears that this is not the case. Ideally, the question would explicitly state that we can cut the bars into smaller pieces but that we can NOT glue smaller pieces together to form larger bars. This seems to be an unstated assumption.

The solution from navami shows that if you CANNOT glue the little extra pieces back together, you need at least 84. You are right that if we could, the answer would be 83.

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