mangamma wrote:

There was a series of two successive discounts of y% on the price of Laptop. The final price of the laptop was tagged at 64% of the original price. What is the value of y?

A) 18%

B) 20%

C) 24%

D) 36%

E) 82%

We can use answer choices and assign an easy number.

Let the laptop's original price = $100

After two successive y discounts, the price is 64% of that $100, so end price = $64

The difference, ($100 - $64) = $36

$36 = the summed dollar value of y at each stage.

That is, the two y discounts in dollars must total $36

Start with (C) to get a benchmark.

If it is too great, we also eliminate D and E, which are greater than C.

If (C) is too small, we eliminate A and B as well.

• Stage 1: Discount and changed priceC) y = 24%24% of $100 = $24 = one of the y dollar amounts to keep

Actual price at end of Stage 1: ($100 - $24) = $76

• Stage 2: Discount and changed priceWe are looking for a discount dollar amount of $12.

Total dollar discount = $36

Stage 1 discount = $24.

Stage 2 discount must therefore = $12

Another 24% must be taken off the new price of $76

• Two ways to handle "24% of $76"

(1) estimate.

24% is about 25% = \(\frac{1}{4}\)

\(\frac{1}{4}\) * $76 = $19

$19 is too great. We need only $12.

Total y + y discount = 24 + 19 = $43 (we need $36)

(2) Do the arithmetic. It's not bad.

24% of $76 = $18.24 = the second y dollar amounts

Add the two y discounts in dollars: $(24 + 18.24) = $42.24

Greater than $36.

y = 24% = Answer C is TOO great.Eliminate C, D, and E

• Option A or B? Use B.

Choose the easier number. Only one of the options is correct.

• Stage 1 discount and changed priceB) y = 20%20% of $100 = $20 = ONE y discount in dollars

New price: ($100 - $20) = $80

• Stage 2 discount and changed price20% of new price of $80 = \((\frac{1}{5}*80)=$16\)

Total dollar discount from Stage 1 + Stage 2:

$(20 + 16) = $36

That's correct.

(As is end price: $100 - $36 = $64,

which is 64% of the original price we assigned,

just as the prompt requires.)

Answer B

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