|
|
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.
15 Feb 2026, 23:48
Kudos
Bookmarks
C
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:
32% (03:20) correct
68%
(02:48)
wrong
based on 34
sessions
History
Date
Time
Result
Not Attempted Yet
Less than 0.3 percent of the chips that Quard produced last week were defective, and exactly 5 percent of the defective chips that Quard produced last week were installed in budget phones. If more than 60 percent of the non-defective chips that Quard produced last week were installed in flagship phones, what is the smallest possible number of chips Quard produced last week that were installed in flagship phones ?
A) 3589
B) 3988
C) 3989
D) 4001
E) 4008
A) 3589
B) 3988
C) 3989
D) 4001
E) 4008
16 Feb 2026, 02:54
Kudos
Bookmarks
This is a classic constraint optimization problem that tests inequality manipulation combined with percent calculations. Here's how to work through it systematically.
Key Concept Being Tested: Working backward from constraints to find minimum/maximum values
Step-by-step solution:
1. Set up your variables
Let T = total chips produced. We need to find the minimum number of chips in flagship phones.
2. Parse the constraints
- Less than 0.3% defective → defective chips < 0.003T
- Exactly 5% of defective went to budget → budget chips = 0.05 × (defective)
- More than 60% of non-defective went to flagship → flagship chips > 0.60 × (non-defective)
3. Express flagship chips mathematically
Flagship chips > 0.60 × (T - defective chips)
4. Minimize flagship by maximizing defective
To minimize flagship phones, we want the smallest possible non-defective count. That means maximizing defective chips. The maximum allowed is just under 0.003T.
5. Work with the boundary condition
At the boundary: defective ≈ 0.003T
So non-defective ≈ 0.997T
Flagship > 0.60 × 0.997T = 0.5982T
6. Find the minimum integer value
We need the smallest T where 0.5982T exceeds one of our answer choices. Testing the answers backward from the smallest:
If flagship = 3989, then T = 3989/0.5982 ≈ 6669 chips total.
Common trap: Students often forget that "more than 60%" means strictly greater than, not ≥. This inequality matters for finding the exact minimum.
Takeaway: When you see "less than," "more than," or "at least" in GMAT problems, always work at the boundary conditions to find min/max values—and watch for whether the inequality is strict or inclusive.
Answer: C) 3989
Key Concept Being Tested: Working backward from constraints to find minimum/maximum values
Step-by-step solution:
1. Set up your variables
Let T = total chips produced. We need to find the minimum number of chips in flagship phones.
2. Parse the constraints
- Less than 0.3% defective → defective chips < 0.003T
- Exactly 5% of defective went to budget → budget chips = 0.05 × (defective)
- More than 60% of non-defective went to flagship → flagship chips > 0.60 × (non-defective)
3. Express flagship chips mathematically
Flagship chips > 0.60 × (T - defective chips)
4. Minimize flagship by maximizing defective
To minimize flagship phones, we want the smallest possible non-defective count. That means maximizing defective chips. The maximum allowed is just under 0.003T.
5. Work with the boundary condition
At the boundary: defective ≈ 0.003T
So non-defective ≈ 0.997T
Flagship > 0.60 × 0.997T = 0.5982T
6. Find the minimum integer value
We need the smallest T where 0.5982T exceeds one of our answer choices. Testing the answers backward from the smallest:
If flagship = 3989, then T = 3989/0.5982 ≈ 6669 chips total.
Common trap: Students often forget that "more than 60%" means strictly greater than, not ≥. This inequality matters for finding the exact minimum.
Takeaway: When you see "less than," "more than," or "at least" in GMAT problems, always work at the boundary conditions to find min/max values—and watch for whether the inequality is strict or inclusive.
Answer: C) 3989
arushi118
Joined: 21 Jul 2024
Last visit: 24 Apr 2026
Posts: 266
Own Kudos:
Given Kudos: 894
Location: India
Concentration: Leadership, General Management
Schools: INSEAD Aug '26 LBS '26 Kellogg '26
GPA: 8.2/10
Products:
17 Feb 2026, 05:53
Kudos
Bookmarks
let total chips = D(defective) + ND(non-defective)
we know that D < 0.3% of total
D < 0.3%*(D+ND)
D < (0.3/100)*(D+ND)
On solving:
99.7D < 0.3ND
997D < 3ND
We know that 5% of D is an integer -> so D should be a multiple of 20
And for minimum chips we will use D = 20
so, ND > (997*20)/3
We also know that F > 60% of ND
F > (60*997*20)/(3*100)
F > 3988
SO minimum F = 3989.
Correct: C
we know that D < 0.3% of total
D < 0.3%*(D+ND)
D < (0.3/100)*(D+ND)
On solving:
99.7D < 0.3ND
997D < 3ND
We know that 5% of D is an integer -> so D should be a multiple of 20
And for minimum chips we will use D = 20
so, ND > (997*20)/3
We also know that F > 60% of ND
F > (60*997*20)/(3*100)
F > 3988
SO minimum F = 3989.
Correct: C
