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Bunuel
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SonalSinha803


I don't understand the meaning of by the yard and how 56/9 is 7 ??

Please explain.

Posted from my mobile device

The term by the yard means wood is sold in quantities like 1 yard, 2 yards, 3 yards, 6 yards, 7 yards etc (always integer value, no decimal values are possible).

As 56/9 = 6.22, one must purchase 7 yards, as decimal value purchase is not possible
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the question stem does not say the wood cannot be sold by partial measure in yard... I do not have this understanding, this question is not very globally applicable IMO.
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faltan
the question stem does not say the wood cannot be sold by partial measure in yard... I do not have this understanding, this question is not very globally applicable IMO.

You are given that wood is sold "by the yard". This means that you cannot buy by partial yard. Imagine the sellers have a scale of a yard only. So they cannot measure 0.2 yards.

Amount of wood needed to make a frame = 4(2/3) feet = 14/3 feet
Amount of wood needed to make 4 frames = (14/3)*4 = 56/3 feet = 56/9 yards (since 3 feet is 1 yard) = 6.2 yards

Wood is sold at $5 a yard (and only by the yard so you cannot buy 0.2 yard). So he will need to buy 7 yards.
Total cost = 5*7 = $35

Answer (D)
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Bunuel
It takes \(4\frac{2}{3}\) feet of wood to make a frame for a lithograph. If wood is sold at $5 a yard and only by the yard, and a collector needs to make 4 frames, how much will the wood cost? (1 yard = 3 feet)


(A) $23.33

(B) $25

(C) $33.33

(D) $35

(E) $100

Solution:

Since 4 frames need to be made, the total number of feet of wood needed is:

4 2/3 x 4 = 16 8/3 = 18 2/3

18 2/3 feet is slightly more than 6 yards; however, since wood is sold only by the yard, we need 7 yards of wood to make the 4 frames. Therefore, we need to by 5 x 7 = $35 worth of wood.

Answer: D
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GMAT takeaway
When you see:

* sold only by the yard
* sold only in whole packages
* must buy whole boxes
Do the calculation first, then round up the quantity before multiplying by price (or adjust the final cost accordingly).
6.22 yards → 7 yards
7 × 5 = 35
Answer: D ($35)


Cost = 5 × (14/3) × (4/3)
because:

* 5 = dollars per yard
* 14/3 = feet per frame
* 4 = frames
* divide by 3 to convert feet to yards
So:
5 × (14 × 4) / 9
= 280/9
= 31.11...
The issue is that 31.11 is the cost if wood could be bought in fractional yards.
But the question says:
"wood is sold at $5 a yard and only by the yard"
You need:
56/9 = 6.22... yards
Since you cannot buy 6.22 yards, you must buy 7 yards.
Therefore:
7 × 5 = 35
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