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Bunuel
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Jamshid and Irwin decided to make up their own version of basketball. 20 Apr 2016, 01:07
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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25% (medium)

Question Stats:

79% (01:25) correct 21% (01:48) wrong based on 219 sessions

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Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets did Irwin score?

A. 0
B. 1
C. 2
D. 3
E. 4
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C
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mathiaskeul
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Jamshid and Irwin decided to make up their own version of basketball. 20 Apr 2016, 02:43
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First thing I noticed was that all these numbers are prime...

Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored 2 11-point baskets in my opinion.

Answer C
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Jamshid and Irwin decided to make up their own version of basketball. 20 Apr 2016, 11:02
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Bunuel
Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets did Irwin score?

A. 0
B. 1
C. 2
D. 3
E. 4
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\(2420\)= \(2^2\) x \(5\) x \(11^2\)

So, Irwin can win 2 , 11 point baskets.
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Jamshid and Irwin decided to make up their own version of basketball. 21 Apr 2016, 11:25
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Arranging the prime factors we can clearly see here that 11^2 is a factor.
hence @
smash C
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Jamshid and Irwin decided to make up their own version of basketball. 21 Apr 2016, 17:19
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2420= (2^2) x (5^1) x (11^2)

So, Irwin can score 2 11-point baskets.
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Jamshid and Irwin decided to make up their own version of basketball. 21 Apr 2016, 20:11
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The answer is 2 (11*11*20)
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Jamshid and Irwin decided to make up their own version of basketball. 01 Aug 2026, 15:06
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Since there is no restriction in number of basket
what if he score 11*5 = 55 (11 baskets with 5 points) 1 with 11 points and 2 with 2 points
Still it would 2420
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Jamshid and Irwin decided to make up their own version of basketball. 03 Aug 2026, 12:06
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Hi Mehta17,

I can see exactly where this slipped. You read "11 five-point baskets" as if it added up to 11 × 5 = 55, but the question multiplies the point values together, not adds them.

So let's actually build your combination as a product:

- 11 baskets worth 5 points each - 5 × 5 × ... × 5 (eleven times) = 511
- 1 basket worth 11 points - × 11
- 2 baskets worth 2 points each - × 2 × 2

That product is 511 × 11 × 4, which is in the tens of millions - nowhere near 2,420. So this combination doesn't actually work.

Why the answer is forced

Here's the deeper reason it's unique: 2,420 breaks into exactly one set of primes.

2,420 = 22 × 5 × 112

Every basket value (2, 5, 11, 13) is either prime or made of these primes, so the point values have to be exactly these factors: two 2's, one 5, and two 11's. There's no freedom - you can't slip in extra 5's, because there's only one5 in 2,420. The 11 appears exactly twice, so Irwin scored two 11-point baskets. That's C.

Quick check to lock it in: try to make 20 as a product of allowed basket values. 20 = 2 × 2 × 5. Could you instead use "two 5-point baskets"? That would need 5 × 5 = 25 ≠ 20. The prime factorization tells you the only breakdown - there's no second option hiding.

Answer: C

Mehta17
Since there is no restriction in number of basket
what if he score 11*5 = 55 (11 baskets with 5 points) 1 with 11 points and 2 with 2 points
Still it would 2420
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