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Posts: 16,400
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
74% (03:42) correct
26%
(03:32)
wrong
based on 934
sessions
History
Date
Time
Result
Not Attempted Yet
Set 1: Red, Blue, Yellow
Set 2: Pink, Turquoise, Orange
Set 3: Purple, Green, Brown
Set 4: Black, White, Silver
A certain company is launching three new products. Color schemes for the packaging are to be selected from colors in the four sets above. Four different colors are needed for each product. For each color scheme, not more than two colors can be selected from one set and colors from not more than three sets can be used.
11.jpg [ 38.9 KiB | Viewed 10103 times ]
Select a color that could be used for the fourth color for all three products. Select a color that could not be used as the fourth color for any of the products.
Set 2: Pink, Turquoise, Orange
Set 3: Purple, Green, Brown
Set 4: Black, White, Silver
A certain company is launching three new products. Color schemes for the packaging are to be selected from colors in the four sets above. Four different colors are needed for each product. For each color scheme, not more than two colors can be selected from one set and colors from not more than three sets can be used.
Attachment:
11.jpg [ 38.9 KiB | Viewed 10103 times ]
Select a color that could be used for the fourth color for all three products. Select a color that could not be used as the fourth color for any of the products.
| Could not be used | Could be used | |
| Orange | ||
| White | ||
| Yellow | ||
| Purple | ||
| Green | ||
| Brown |
GMAT 1: 710 Q50 V36
Posts: 7
help! any explaination?
Posts: 16,400
Official Explanation
The fourth color could be orange for all three since for product 1 it cannot be purple, green or brown or yellow; for product 2 it cannot be yellow, and it cannot be white as product 2 already uses white; for product 3 it cannot be red, blue or yellow. From this information we can also see that a color that would not be suitable to complete any of the color schemes is yellow.
The fourth color could be orange for all three since for product 1 it cannot be purple, green or brown or yellow; for product 2 it cannot be yellow, and it cannot be white as product 2 already uses white; for product 3 it cannot be red, blue or yellow. From this information we can also see that a color that would not be suitable to complete any of the color schemes is yellow.
Product 1 Product 2 Product 3
Yellow (S1) Blue (S1) Green (S3)
Pink (S2) White (S4) Silver (S4)
Silver (S4) Red (S1) Turquoise (S2)
4th color in P1 => S1, S2 or S4
4th color in P2 => Cannot be S1
4th color in P3 => S2, S3, or S4
Could not be used
S1 color could not be used in P2 and P3
=> Find an S1 color in P1
=> Yellow
Could be used
Could be used must be either S2 or S4
P1 => Cannot be Pink or Silver
P2 => Cannot be White
P3 => Cannot be Silver and Turqoise
=> Only Orange and Black left
=> Orange
Yellow (S1) Blue (S1) Green (S3)
Pink (S2) White (S4) Silver (S4)
Silver (S4) Red (S1) Turquoise (S2)
4th color in P1 => S1, S2 or S4
4th color in P2 => Cannot be S1
4th color in P3 => S2, S3, or S4
Could not be used
S1 color could not be used in P2 and P3
=> Find an S1 color in P1
=> Yellow
Could be used
Could be used must be either S2 or S4
P1 => Cannot be Pink or Silver
P2 => Cannot be White
P3 => Cannot be Silver and Turqoise
=> Only Orange and Black left
=> Orange
This is a poor quality question
pratiksha1998
Joined: 11 Aug 2021
Last visit: 09 Jul 2026
Posts: 93
Location: India
Concentration: General Management, Strategy
Schools: Goizueta '25
GMAT 1: 600 Q47 V27
For, could not be used, Brown can also be an answer right?
pratiksha1998
Brown can be used in Product 3
What would be the faster approach?
Solving all cases and then verifying options or checking all options one by one?
TPA questions generally seem to be time consuming.
Solving all cases and then verifying options or checking all options one by one?
TPA questions generally seem to be time consuming.
Sajjad1994
The best is actually a combination of both.
You would start with analyzing all 3 products to identify:
[*]Which sets are used in each product
[*]How many colors per set are used (for the "max 2 per set" rule)
Step 2: Check Each Option With This New Info:
Now you can go through options quickly, checking whether the color’s set:
Because you already pre-mapped constraints, it becomes a simple yes/no check per option (5–10 seconds each).
You would start with analyzing all 3 products to identify:
[*]Which sets are used in each product
[*]How many colors per set are used (for the "max 2 per set" rule)
Step 2: Check Each Option With This New Info:
Now you can go through options quickly, checking whether the color’s set:
- Is allowed (not a 4th set)
- Is under limit (max 2 per set)
Because you already pre-mapped constraints, it becomes a simple yes/no check per option (5–10 seconds each).
SaiJ1011
Stormik1
Joined: 24 May 2026
Last visit: 14 Sep 2026
Posts: 33
Location: India
Schools: HEC Sept '27 INSEAD Aug '27 LBS '27 ISB
GPA: 8.9
Products:
Schools: HEC Sept '27 INSEAD Aug '27 LBS '27 ISB
Posts: 33
how to select between orange, purple & brown for 'could be used' ?
Posts: 5
I’d treat each product as needing 4 colors, with no more than 2 from any set and at least 2 sets involved. The main thing is counting valid combinations carefully.
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