Less than 0.3 percent of the chips produced at a certain factory last

Question

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

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Official Answer

C

A) 3589
B) 3988
C) 3989
D) 4001
E) 4008

Edskore · Answer

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

arushi118 · Answer

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

kevincan · Answer

Suppose x chips were produced , d of which were defective .

d < 3x/ 1000 and thus x > 1000d/3

d/20 defective chips were installed in budget phones. Thus d is a multiple of 20, i.e d =20k for some positive integer k

So we can write that

x > 1000d/3 > 20000k/3

Therefore, the smallest possible value of x is 6667 and the smallest possible value of x - d is 6647

Given that more than 60 percent of x - d were installed in flagships and that 6647 * 0.6 =3988.2 , choose 3989

Less than 0.3 percent of the chips produced at a certain factory last

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Less than 0.3 percent of the chips produced at a certain factory last

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