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GRE Quantitative · Question 14
How many ways can you select 2 items from a group of 7?
Your mistake
You calculated 6 × 7 = 42 (a simple product) instead of using the combination formula.
Correct approach
This is a selection problem (order doesn't matter), so use C(7,2) = 7! / (2! × 5!) = 21.
Key concept
Use combinations C(n,r) when order doesn't matter. Use permutations P(n,r) when it does.
Pattern detected
You've confused multiplication with combinations 3 times this week.
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How many ways can you select 2 items from a group of 7?
Your mistake
You multiplied 6 × 7 instead of using combinations for selection without order.
Correct approach
Use C(7,2) = 7! / (2! × 5!) = 21.
An item is discounted by 20% and then by 10%. What is the net discount?
Your mistake
You added the discounts directly (20 + 10) instead of applying them sequentially.
Correct approach
Net multiplier = 0.8 × 0.9 = 0.72, so discount = 28%.
What is the time complexity of binary search on a sorted array of n elements?
Your mistake
You mapped it to linear scan, but binary search discards half the space each step.
Correct approach
Search interval halves repeatedly, giving O(log n).
The author says urban gardens are "supplementary, not substitutive". This implies:
Your mistake
You selected an extreme interpretation that contradicts the phrase "not substitutive".
Correct approach
The sentence supports a balanced inference: useful support, not complete replacement.
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"You got 42 because you used 6×7 instead of C(7,2)." The exact mistake, not just the answer.
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