If the recommended weight w, in pounds, for a male… GMAT

If the recommended weight w, in pounds, for a male… GMAT Data Sufficiency Question

Here’s the question for you:

If the recommended weight w, in pounds, for a male is given in terms of his height h, 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.

In analyzing this question, read each individual part separately. Note how the w-term is predicated on the h-term. In other words, the weight is relative to the height, or as the height changes, so does the weight.

What we see, then, is that in order to know Eric’s recommended weight relative to Tom’s, we need to know Eric’s height relative to Tom’s.

The question, however, is whether we need to know Eric’s absolute height–that is, an actual fixed value–or whether we simply need to know the relative height, or the difference between his and Tom’s heights.

In any case, we need to be able to relate the two heights or we have effectively no relevant information. 

If we look at what’s given in the question stem, we get the formula w = 4.5h − 154. Great–this is something to work with. If we get a fixed value for one, we can get the fixed value for the other. The only other question, then, is relative values.

Statement 1 tells us that Eric is 4 inches taller than Tom. Let’s plug into the equation to see what happens: 

Let’s then call Tom’s height t and Eric’s height t + 4. We can call Tom’s recommended weight w_t and Eric’s recommended weight w_e. This gives us the following:

w_t = 4.5t − 154

w_e = 4.5(t+4) − 154 = 4.5t + 18 – 154 = 4.5t – 136

As you can see, we then get Eric’s weight relative to Tom’s height and a corresponding weight for each of them, all in terms of Tom’s height. This is SUFFICIEENT.

Remember that Statement 2 has a greater burden at this point given that Statement 1 solves independently. Statement 2 must solve independently for D; otherwise the answer is A. 

In this case, you’ll note that we have no mention of Eric’s height or how much he weighs, so we have no way to relate Eric to Tom. This will not work. INSUFFICIENT. 

The answer is A. 

Luckily, for other “if the recommended weight w, in pounds, for a male…” questions will be roughly similar to this one.

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