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555-605 (Medium)|   Arithmetic|   Word Problems|            
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kaptainklutz
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Last month a certain music club offered a discount to 11 Feb 2023, 12:42
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Bunuel
SOLUTION

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid $3.99 for each additional compact disc purchased. If a preferred customer purchased a total of 6 compact discs and paid $15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following?

(A) 5(4.00) + 15.90
(B) 5(4.00) + 15.95
(C) 5(4.00) + 16.00
(D) 5(4.00 - 0.01) + 15.90
(E) 5(4.00 - 0.05) + 15.95

The cost of 6 compact discs would be $15.95 for the first compact disc plus $3.99 for each of the other 5 discs, so it's \($15.95+5*$3.99\).

We can see that no answer choice matches this value. So, we should manipulate with that expression to get the answer which is listed.

\($15.95+5*$3.99=15.95+5*(4-0.01)=15.95+5*4-0.05=5*4+15.90\).

Answer: A.

Difficulty level changed to 600.
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I was a little confused on why shouldn't it be C. From what I understand, the total price is supposed to be 5*3.99 + 15.95. Now Option C tells us 5*(4) + 16 which can be rewritten as 5*(3.99-0.01) + 16 = 5*3.99 - 0.05 + 16 = 5*3.99 + 15.95 which is what our initial calculation said. Option A on opening the parenthesis would give us 4*3.99 + 15.85. So shoudn't it be C ?
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Last month a certain music club offered a discount to 11 Feb 2023, 12:54
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kaptainklutz
Bunuel
SOLUTION

Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid $3.99 for each additional compact disc purchased. If a preferred customer purchased a total of 6 compact discs and paid $15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following?

(A) 5(4.00) + 15.90
(B) 5(4.00) + 15.95
(C) 5(4.00) + 16.00
(D) 5(4.00 - 0.01) + 15.90
(E) 5(4.00 - 0.05) + 15.95

The cost of 6 compact discs would be $15.95 for the first compact disc plus $3.99 for each of the other 5 discs, so it's \($15.95+5*$3.99\).

We can see that no answer choice matches this value. So, we should manipulate with that expression to get the answer which is listed.

\($15.95+5*$3.99=15.95+5*(4-0.01)=15.95+5*4-0.05=5*4+15.90\).

Answer: A.

Difficulty level changed to 600.

I was a little confused on why shouldn't it be C. From what I understand, the total price is supposed to be 5*3.99 + 15.95. Now Option C tells us 5*(4) + 16 which can be rewritten as 5*(3.99-0.01) + 16 = 5*3.99 - 0.05 + 16 = 5*3.99 + 15.95 which is what our initial calculation said. Option A on opening the parenthesis would give us 4*3.99 + 15.85. So shoudn't it be C ?
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The point is 4 does not equal to 3.99 - 0.01.
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Last month a certain music club offered a discount to 29 May 2024, 20:32
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Last month a certain music club offered a discount to 02 Oct 2025, 06:12
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This is a classic GMAT word problem that tests your ability to translate a scenario into mathematical expressions. Let me walk you through how to tackle this step by step.

The key insight here is understanding what "equivalent" means - you're not looking for the exact expression, but one that gives the same total value.

Step 1: Break down what actually happened

Let's think about this carefully. The customer bought 6 CDs total:
- First CD cost: \(\$15.95\)
- Each additional CD cost: \(\$3.99\)
- Number of additional CDs: \(6 - 1 = 5\) CDs

Notice how I said "additional" - this means after the first one. This is a common trap students fall into.

Step 2: Calculate the actual total cost

Here's what the customer actually paid:
- Cost of first CD: \(\$15.95\)
- Cost of 5 additional CDs: \(5 \times \$3.99 = \$19.95\)
- Total cost: \(\$15.95 + \$19.95 = \$35.90\)

So the customer paid exactly \(\$35.90\).

Step 3: Test each answer choice

Now here's where it gets interesting. Let's see which expression equals \(\$35.90\):

(A) \(5(4.00) + 15.90 = 20.00 + 15.90 = 35.90\) ✓
(B) \(5(4.00) + 15.95 = 20.00 + 15.95 = 35.95\)
(C) \(5(4.00) + 16.00 = 20.00 + 16.00 = 36.00\)

The answer is (A).

Here's what you need to see: Choice (A) rounds \(\$3.99\) up to \(\$4.00\) and rounds \(\$15.95\) down to \(\$15.90\). These small adjustments perfectly cancel each other out, giving us the exact total of \(\$35.90\).

The question asks for an "equivalent" expression, which means approximations that yield the same result are perfectly acceptable.

---

You can check out the complete systematic framework on Neuron by e-GMAT to master word problem translation and recognize the patterns that appear across similar official questions. You can also explore detailed solutions for other GMAT official questions on Neuron with step-by-step breakdowns and common trap identification.
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Last month a certain music club offered a discount to 03 Mar 2026, 09:57
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Bunuel
Last month a certain music club offered a discount to preferred customers. After the first compact disc purchased, preferred customers paid $3.99 for each additional compact disc purchased. If a preferred customer purchased a total of 6 compact discs and paid $15.95 for the first compact disc, then the dollar amount that the customer paid for the 6 compact discs is equivalent to which of the following?

(A) 5(4.00) + 15.90
(B) 5(4.00) + 15.95
(C) 5(4.00) + 16.00
(D) 5(4.00 - 0.01) + 15.90
(E) 5(4.00 - 0.05) + 15.95
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