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josiewhoasie
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Bob expected to spend a total of $9.00 to buy a given amount of pasta 05 Mar 2025, 18:53
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Hi avigutman, thanks for this very helpful answer.

I can't figure out where you're getting the "so he would've been able to buy 10/9 as many pounds if the price were as he expected it to be" number. Can you help me understand? Even chatgpt couldn't figure it out. :P

Thanks so much in advance!
avigutman
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avigutman - Can you please share a reasoning based approach to this question.
Obscurus this is a rare question type for which you either have to solve a quadratic equation (which I don't recommend) or use the answer choices (the better approach in my opinion). Firstly, how to recognize this question type?

When you have the product of two positive numbers (a and b), and you're told that the same product can be reached by adding to one of the numbers and subtracting from the other [(a+x)(b-y), where x and y are positive numbers]. Importantly, we don't know the ratio a:(a+x) nor b:(b-y). If we do know one of those ratios, we can solve using a beautiful reasoning based solution.

Some other official questions in this rare category:
https://gmatclub.com/forum/a-store-curr ... 44780.html
https://gmatclub.com/forum/a-boat-trave ... ml#p778643
https://gmatclub.com/forum/at-his-regul ... 36642.html

The non-integer answer choices make this particular problem more challenging (similar to the boat problem) but we know that the GMAT isn't all that interested in testing our ability to do lots of complicated math in a 2-minute-per-question setting, so it's likely that the answer choice that's easiest to check is the correct answer choice (as is the case in both the boat question and this question).

How I approached this problem: the answer choices represent Bob's cost/pound, and I know he expected to spend 20 cents less than that. Which answer choice is easiest to subtract 20 cents from? Well, (E) looks good to me because it's easy to divide $9 by $2, and also "20 cents less" is exactly 10% below. In other words, he expected to spend 9/10 as much as he did, so he would've been able to buy 10/9 as many pounds if the price were as he expected it to be (this is me using ratios for a beautiful reasoning-based approach).

At $2/pound he bought 4.5 pounds, and 10/9 of 4.5 pounds is exactly 5 pounds - that's the 1/2 pound difference that we were expecting. Done!

Can you imagine having to divide $9 by any of the other answer choices?? It's unlikely that we'd have to do that on the GMAT (unless that was the entire question).
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Bob expected to spend a total of $9.00 to buy a given amount of pasta 15 Jun 2025, 20:34
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This is a trick I learned from another GMAT Club Answer.

The difference between the price and what Bob is paying is $0.2

1. We check the answer choices which have the above difference
2. Eliminate all other choices. Which leaves with $1.8 and $2.0
3. GMAT expects you to make a mistake of choosing the option of how much the price of a salad actually is, expects you to pick 1.8 but Bob is paying $0.2 more, hence the answer is 2.0
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Bob expected to spend a total of $9.00 to buy a given amount of pasta 15 Jun 2025, 22:18
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Bob expected to spend a total of $9.00 to buy a given amount of pasta salad at a fixed price per pound. However, the price of the salad was $0.20 more per pound than Bob had expected. Consequently, he spent $9.00 and bought \(\frac{1}{2}\) pound less of the salad. How much did Bob spend per pound for the salad?

A. $1.80
B. $1.85
C. $1.90
D. $1.95
E. $2.00

Hello, people. Let's get into this.

For this question, you may find it easier to simply test the values provided in the answer options after understanding what is going on in the prompt. Basically, Bob thought he was going to get a certain number of pounds of pasta, but because the cost per pound was $0.20 higher than he thought, he ended up with half a pound less.

Let's test Option (A):

$9 / $1.8 = 5 pounds

Remember, Bob got half a pound less than he expected. So, if we reduce the price per pound by $0.20, for this to be the correct answer, we should get half a pound more: 5.5 pounds.

But is $9 / $1.6 = 5.5 pounds?

No, it's 5.625 pounds. Therefore, this can't be the correct answer.

Similarly test the other options...

When you test Option (E):

$9 / $2 = 4.5 pounds

We're therefore testing whether we get 5 pounds if the price per pound were $0.20 lower.

Is $9 / $1.8 = 5 pounds?

Yes, therefore (E) is your answer.
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Bob expected to spend a total of $9.00 to buy a given amount of pasta 24 Sep 2025, 18:07
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I don't know if this is still relevant. But just wanted to point it out that, there are pattern to almost all gmat official questions. This particular question has quite a number of similar question. You just need to learn to internalise each question that you solve. You don't just solve question. You solve and learn the reasoning behind it. This is how your brain learn to trace the pattern and be able to think fast when you come across similar question.
Honeybadger269

­Highly elegant and intricate explanation.

Are there people who a] are not naturally good at 'math' and b] have learnt to think and execute this stuff within the time constraints and under the exam pressure by way of GMAT preparation? If yes, please reply to this and tell me how you developed this skill. I have been preparing for the test for a long time and still can never do this in any mock or actual attempt.

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Bob expected to spend a total of $9.00 to buy a given amount of pasta 11 Jul 2026, 09:09
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The GMAT wants you to turn sentences into equations. Or in this case, two equations.

Let the price per pound of salad = p. We want to solve for p... though keep in mind that we ultimately want to find p + .20

Let the number of pounds = x

9 = px
and
9 = (p + .2)(x - .5)

Now, sometimes the quickest way to solve a problem is by "backsolving", i.e. plugging answer choices into the equation. If you give it a try, some high-scoring students might see what's going on, but it's not obvious in this case, so we'll switch gears and jump into the algebra.

Combine the two equations:

px = (p + .2)(x - .5)

Now, this question is maddening for a few reasons. The first is that it's easy to make simple mistakes under time pressure, especially since decimals are involved.

Let's re-write the right-hand side of the equation

px = px -.5p + .2x - .1

Simplify by subtracting px from both sides:

0 = -.5p +.2x -.1

re-arrange

0 = .2x - .5p -.1

To make life easier, let's get rid of decimals. Multiply both sides of the equation by 10

0 = 2x - 5p - 1

The GMAT now wants you to recognize that, in order to answer the question, we want to use this equation to isolate x, and then ultimately plug that into first equation, which was 9 = px

So first we'll solve for x:

0 = 2x - 5p - 1

5p + 1 = 2x

(5p +1)/2 = x

Now the second maddening part: if you plug that x value into the original equation, 9 = px, you have

9 = p * (5p +1)/2

"distribute" the p:

9 = (5p^2 + p)/2

18 = 5p^2 + p

To find p, set it all of this equal to zero, then factor (which is not necessarily easy to do under timed conditions, since we have a 5p^2 in our hands)

0 = 5p^2 + p - 18

0 = (5p - 9)(p + 2)

Since p cannot be a negative number, it can't be -2. So now we'll find the value for p when 5p - 9 = 0

p = 9/5 = 1.8

So the answer is $1.80, right? No! Always, always, always re-read a question before you submit an answer. The question wants us to find p + .20, which is $2.00

Answer E

Going back to the initial approach, which was backsolving, high-scoring students might have noticed that you don't want to plug the answer choices into the 9 = px equation, you want to plug them into the 9 = (p + .2)(x - .5) equation. If you plug $1.80 into that equation, you'll see that x - .5 = 4.5 pounds. Which means x in the 9 = px equation = 5 pounds, which means that, yes, p would have been $1.80. Which means the correct answer to the question (p + .20) is $2.00. Not so obvious in this case, but backsolving is a reasonable approach that you certainly want to keep in mind in the future.
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