Riya plans to order 95 custom shirts for the participants of a fundraising event she is organizing. She is considering two options for ordering the shirts—a local option where she would have no shipping costs and an option to order the shirts online and have them shipped to her. If she uses the local option, each shirt will cost $x . If she uses the online option, each shirt will cost slightly less, at $y , but she will have to pay a flat shipping fee of $22 . These are the only costs associated with ordering the shirts. Riya correctly determined that by ordering the 95 shirts using the online option rather than the local option, she will spend exactly $16 less.

Riya plans to order 95 custom shirts for the participants of a fundraising event she is organizing. She is considering...

GMAT Two Part Analysis : (TPA) Questions

Source: Mock

Two Part Analysis

Quant - Fitting Values

HARD

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Riya plans to order 95 custom shirts for the participants of a fundraising event she is organizing. She is considering two options for ordering the shirts—a local option where she would have no shipping costs and an option to order the shirts online and have them shipped to her. If she uses the local option, each shirt will cost $\mathrm{\$x}$. If she uses the online option, each shirt will cost slightly less, at $\mathrm{\$y}$, but she will have to pay a flat shipping fee of $\mathrm{\$22}$. These are the only costs associated with ordering the shirts. Riya correctly determined that by ordering the 95 shirts using the online option rather than the local option, she will spend exactly $\mathrm{\$16}$ less.

Select a value for $\mathrm{x}$ and a value for $\mathrm{y}$ that are jointly consistent with the information provided. Make only two selections, one in each column.

12.04

12.10

12.25

12.33

12.50

Solution

Phase 1: Owning the Dataset

Visual Representation

Since we're comparing two options with different cost structures, let's use a comparison table:

Option	Per Shirt Cost	Shipping	Total Cost (95 shirts)
Local	$x	$0	$95\mathrm{x}$
Online	$y	$22	$95\mathrm{y} + 22$

Key constraint: Online total is exactly $16 less than Local total

Phase 2: Understanding the Question

Breaking Down the Relationship

We're told that ordering online saves exactly $16. Let's translate this:

Local cost = $95\mathrm{x}$
Online cost = $95\mathrm{y} + 22$
Online is $16 less, so: Online cost = Local cost - 16

This gives us: $95\mathrm{y} + 22 = 95\mathrm{x} - 16$

Simplifying to Find the Key Relationship

$95\mathrm{y} + 22 = 95\mathrm{x} - 16$
$95\mathrm{y} = 95\mathrm{x} - 16 - 22$
$95\mathrm{y} = 95\mathrm{x} - 38$
$\mathrm{y} = \mathrm{x} - \frac{38}{95}$

Using calculator for precision: $38 ÷ 95 = 0.4$

Key insight: $\mathrm{y} = \mathrm{x} - 0.40$

This means the online per-shirt price is exactly $0.40 less than the local price.

Phase 3: Finding the Answer

Systematic Check of Options

Given choices: 12.04, 12.10, 12.25, 12.33, 12.50

We need x and y where $\mathrm{y} = \mathrm{x} - 0.40$. Let's check each potential x value:

If x = 12.04 → y = 12.04 - 0.40 = 11.64 (not in choices)
If x = 12.10 → y = 12.10 - 0.40 = 11.70 (not in choices)
If x = 12.25 → y = 12.25 - 0.40 = 11.85 (not in choices)
If x = 12.33 → y = 12.33 - 0.40 = 11.93 (not in choices)
If x = 12.50 → y = 12.50 - 0.40 = 12.10 ✓ (12.10 is in choices!)

? Stop here - we found our answer.

Verification

Let's confirm our answer works:

Local cost: $95 × \$12.50 = \$1,187.50$
Online cost: $95 × \$12.10 + \$22 = \$1,149.50 + \$22 = \$1,171.50$
Savings: $\$1,187.50 - \$1,171.50 = \$16$ ✓

Phase 4: Solution

Final Answer:

$\mathrm{x} = \$12.50$ (local per-shirt cost)
$\mathrm{y} = \$12.10$ (online per-shirt cost)

These values satisfy our requirement that $\mathrm{y} = \mathrm{x} - 0.40$ and result in exactly $16 savings when ordering 95 shirts online versus locally.

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