The number of tests that the group should buy?

[email protected] wrote:Hi Sri,

You absolutely had the right idea, you just have to take it a step further.

We're told that the two tests cost $20 and $30 AND that we want to spend an EQUAL AMOUNT of money on each.

The LCM of 20 and 30 is 60, so imagine if you spent $60 on each test….

You'd get 3 Fossil Ease Tests and 2 Dino Diagnosis Tests.

This gives us a RATIO of what the correct answer has to be…..3:2

Now, pick two numbers from the given options that end in a 3:2 ratio…

Final Answer: [spoiler]FE = 150, DD = 100[/spoiler]

GMAT assassins aren't born, they're made,
Rich

Hi Rich,

Thanks a lot for the explanation.

Best Regards,
Sri

ok thanks gmattesttaker2




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What we see: a Two-Part Analysis question. Fossil Ease tests cost $20, Dino Diagnosis tests cost $30, and the group spends the same amount on each brand. We pick one number of tests for each brand.

Step 1. Turn "equal amount of money" into an equation.
What we see: \(F\) Fossil Ease tests cost \(20F\) dollars; \(D\) Dino Diagnosis tests cost \(30D\) dollars.
What it means: \(20F = 30D\), so \(2F = 3D\), and \(\frac{F}{D} = \frac{3}{2}\).
What we do and why: the cheaper test must be bought in larger numbers. For every 3 Fossil Ease tests, buy 2 Dino Diagnosis tests.

Step 2. Find the pair in the list with a 3 to 2 ratio.
What we see: the choices are 100, 150, 200, 250 and 400.
What it means: we need Fossil Ease \(= 1.5 \times\) Dino Diagnosis, with both numbers in the list.
What we do and why: try each Dino Diagnosis number. 100 gives 150 (in the list). 200 gives 300 (not in the list). 250 gives 375 (no). 400 gives 600 (no). 150 gives 225 (no). Only one pair works: Fossil Ease 150, Dino Diagnosis 100.

Step 3. Check.
\(150 \times 20 = 3{,}000\) dollars and \(100 \times 30 = 3{,}000\) dollars. Equal.

The trap: swapping the columns (Fossil Ease 100, Dino Diagnosis 150). The 3 to 2 ratio feels like it belongs to the $30 test because 30 is bigger, but the cheaper test needs the bigger count to reach the same total.
Faster way: same money means the counts go in the opposite ratio of the prices. Prices are 20 to 30, so counts are 30 to 20, which is 3 to 2.
Takeaway: when two things share the same total spend, the number bought goes opposite to the price: cheaper item, more units.

Answer: Fossil Ease 150, Dino Diagnosis 100