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.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2512:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
38% (02:57) correct
62%
(03:11)
wrong
based on 37
sessions
History
Date
Time
Result
Not Attempted Yet
Gustavo’s Gym plans to purchase weight plates in four sizes: 1 pound, 5 pounds, 10 pounds, and 25 pounds. The plates cost $1, $8, $24, and $100, respectively. The gym wants to purchase plates so that every integer weight from 1 pound to 100 pounds can be assembled using some subset of the purchased plates, using each purchased plate at most once. If the total cost of the plates must be less than $350, what is the smallest number of plates Gustavo’s gym can purchase?
A. 10
B. 11
C. 12
D. 13
E. 14
A. 10
B. 11
C. 12
D. 13
E. 14
07 Mar 2026, 01:03
Kudos
Bookmarks
Key Concept: Minimum Set Coverage with a Budget Constraint
This is one of the more satisfying hard PS problems because it combines two constraints simultaneously — coverage (can you assemble every integer weight from 1 to 100?) and cost (total spend < $350). The mistake most people make is either testing one constraint at a time or going straight for three 25-lb plates without checking if the budget holds.
Step 1 — Understand what "coverage" means:
Every integer weight 1–100 must be achievable by picking some subset of the purchased plates. Each purchased plate can be used at most once per assembly. So if you buy three 10-lb plates, you can assemble 10, 20, or 30 — but not 40.
Step 2 — Anchor the small values first:
To make 1, 2, 3, 4 you need at least four 1-lb plates ($4 total). With any fewer, there's a gap in the low values — for example, with only two 1s, you can't assemble 3.
Step 3 — Build up the range with 5s and 10s:
With {4×(1lb), 1×(5lb)}: you can cover 1–9. Adding each 10-lb plate extends coverage by 10 (1×10 covers 10–19, 2×10 covers 20–29, etc.). To reliably reach the 90s you need four 10-lb plates. Cost so far: $4 + $8 + 4×$24 = $108.
Step 4 — Push coverage to 100 with 25-lb plates:
With 4×10 maxing out at 40 (from 10s alone), adding two 25-lb plates gives a ceiling of 50+40+9 = 99. Can you make 100? 25+25+10+10+10+10+5+4×1 = 100. ✓
Total plates: 4+1+4+2 = 11 plates. Cost: $4+$8+$96+$200 = $308 < $350. ✓
Step 5 — Can you do it in 10?
Any 10-plate combination runs into trouble. For example, swapping one 10-lb plate for a third 25-lb plate: three 25s cost $300, leaving only $49 for everything else — not enough 10-lb plates to bridge coverage gaps in the 60–90 range. Other 10-plate combos either exceed $350 or leave an uncoverable value.
Answer: B (11)
Common trap: Immediately going for three 25-lb plates to maximize range. Three 25s cost $300 alone, leaving only $49 for the remaining plates — not enough 10s to fill the middle gaps.
Takeaway: In min-max coverage problems, work from the bottom up — lock in small-value coverage first, then layer up with larger plates while tracking the cost ceiling.
This is one of the more satisfying hard PS problems because it combines two constraints simultaneously — coverage (can you assemble every integer weight from 1 to 100?) and cost (total spend < $350). The mistake most people make is either testing one constraint at a time or going straight for three 25-lb plates without checking if the budget holds.
Step 1 — Understand what "coverage" means:
Every integer weight 1–100 must be achievable by picking some subset of the purchased plates. Each purchased plate can be used at most once per assembly. So if you buy three 10-lb plates, you can assemble 10, 20, or 30 — but not 40.
Step 2 — Anchor the small values first:
To make 1, 2, 3, 4 you need at least four 1-lb plates ($4 total). With any fewer, there's a gap in the low values — for example, with only two 1s, you can't assemble 3.
Step 3 — Build up the range with 5s and 10s:
With {4×(1lb), 1×(5lb)}: you can cover 1–9. Adding each 10-lb plate extends coverage by 10 (1×10 covers 10–19, 2×10 covers 20–29, etc.). To reliably reach the 90s you need four 10-lb plates. Cost so far: $4 + $8 + 4×$24 = $108.
Step 4 — Push coverage to 100 with 25-lb plates:
With 4×10 maxing out at 40 (from 10s alone), adding two 25-lb plates gives a ceiling of 50+40+9 = 99. Can you make 100? 25+25+10+10+10+10+5+4×1 = 100. ✓
Total plates: 4+1+4+2 = 11 plates. Cost: $4+$8+$96+$200 = $308 < $350. ✓
Step 5 — Can you do it in 10?
Any 10-plate combination runs into trouble. For example, swapping one 10-lb plate for a third 25-lb plate: three 25s cost $300, leaving only $49 for everything else — not enough 10-lb plates to bridge coverage gaps in the 60–90 range. Other 10-plate combos either exceed $350 or leave an uncoverable value.
Answer: B (11)
Common trap: Immediately going for three 25-lb plates to maximize range. Three 25s cost $300 alone, leaving only $49 for the remaining plates — not enough 10s to fill the middle gaps.
Takeaway: In min-max coverage problems, work from the bottom up — lock in small-value coverage first, then layer up with larger plates while tracking the cost ceiling.
07 Mar 2026, 01:18
Kudos
Bookmarks
Almost perfect, the only trouble is that no combination of 11 weights will produce a total weight of 100. I may have to add the word inclusive.
