Forum Home > GMAT > Quantitative > Problem Solving (PS)
Events & Promotions
|
|
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Jan 2410:00 AM EST
-12:00 PM EST
The Target Test Prep team is proud to introduce GMAT OnDemand, a video course created by Scott Woodbury-Stewart, founder and CEO, designed to provide you with everything you need to master the GMAT and achieve your score goals.
Jan 2110:00 AM PST
-11:59 PM PST
For a limited time, get 20% off our GMAT courses, including private tutoring! Work with an expert who will help you ace the GMAT and achieve your dreams. Use code 20NEW.
Jan 2511:00 AM IST
-01:00 PM IST
Attend this session to learn how to Deconstruct arguments, Pre-Think Author’s Assumptions, and apply Negation Test.- Jan 26
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease.
15 Jul 2023, 06:19
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
66% (02:47) correct
34%
(03:12)
wrong
based on 721
sessions
History
Date
Time
Result
Not Attempted Yet
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
A. $1.80
B. $1.85
C. $1.90
D. $1.95
E. $2.00
avigutman
Tutor
Joined: 17 Jul 2019
Last visit: 03 Oct 2024
Posts: 1,297
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert reply
16 Jul 2023, 05:30
Kudos
Bookmarks
Obscurus
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).
15 Jul 2023, 15:33
Kudos
Bookmarks
gmatophobia
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. \($2.00 \)
A. \($1.80 \)
B. \($1.85 \)
C. \($1.90 \)
D. \($1.95 \)
E. \($2.00 \)
He expected to spend $9 to buy q pounds of salad at p dollars per pound:
Total cost = p × q = $9
However, things turned out differently for him:
Total cost = (p + 0.2) × (q - 0.5) = $9
Let’s solve the system of equations for p.
(p + 0.2) × (q - 0.5) = p × q
pq + 0.2q – 0.5p – 0.1 = pq
0.2q – 0.5p – 0.1 = 0
2q – 5p – 1 = 0
q = (5p + 1)/2
Now we can substitute the above expression for q in the first equation.
p × (5p + 1)/2 = 9
5p^2 + p – 18 = 0
(5p – 9)(p + 2) = 0
If p + 2 = 0, then p = -2, which is an invalid case.
If 5p – 9 = 0, then p = 9/5 = 1.8.
Therefore, he paid 1.8 + 0.2 = $2 per pound for the salad.
Answer: E
