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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