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If the recommended weight w

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by NandishSS » Mon Dec 19, 2016 9:40 am
If the recommended weight w, in pounds, for a male is given in terms of his height hh, in inches, by the formula w=4.5h−154, how much greater is Eric's recommended weight than Tom's, according to this formula?

(1) Eric is 4 inches taller than Tom.

(2) According to the formula, Tom's recommended weight is 152 pounds.

OA:A

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by DavidG@VeritasPrep » Mon Dec 19, 2016 12:24 pm
NandishSS wrote:If the recommended weight w, in pounds, for a male is given in terms of his height hh, in inches, by the formula w=4.5h−154, how much greater is Eric's recommended weight than Tom's, according to this formula?

(1) Eric is 4 inches taller than Tom.

(2) According to the formula, Tom's recommended weight is 152 pounds.

OA:A

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You can see immediately that statement 2 alone is not sufficient. Knowing Tom's recommended weight gives us nothing about Eric's. So let's dig into statement 1.

Call Tom's height: T
Eric's height: T + 4

Tom's rec weight: 4.5(T)−154
Eric's rec weight: 4.5(T + 4) - 154

The difference: 4.5(T+4) - 154 - [4.5(T) -154]
= 4.5T + 18 -154 - 4.5T + 154 (terms in red cancel out)
=18. So sufficient. The answer is A.

(But as soon as you see that the t's will cancel out, you know you'll get a unique value.)
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by [email protected] » Mon Dec 19, 2016 8:17 pm
Hi NandishSS,

As David has pointed out - in this prompt, Fact 2 is clearly insufficient. Thus, it's really a matter of how efficiently you can deal with the information in Fact 1. It's important to note that the prompt is NOT asking for Eric's recommend weight and Tom's recommended weight - it's asking for the DIFFERENCE in their recommended weights. The phrasing in that question implies that there might be a relationship in those two values that we can look for...

1) Eric is 4 inches taller than Tom.

Let's TEST VALUES to see if a pattern emerges....

IF....
Eric = 100 inches tall... his recommended weight = (4.5)(100) - 154 = 450 - 154 = 296 pounds
Tom = 96 inches tall... his recommended weight = (4.5)(96) - 154 = 434 - 154 = 280 pounds
The difference = 296 - 280 = 16 pounds

IF....
Eric = 104 inches tall... his recommended weight = (4.5)(104) - 154 = 466 - 154 = 312 pounds
Tom = 100 inches tall... his recommended weight = (4.5)(100) - 154 = 450 - 154 = 296 pounds
The difference = 312 - 296 = 16 pounds

It certainly appears that there's a 'consistency' here...and if you TEST any additional pairs of weights, you will find that the DIFFERENCE is ALWAYS 16 pounds. Thus, the answer is ALWAYS 16 pounds.
Fact 1 is SUFFICIENT

Final Answer: A

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