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There was a series of two successive discounts of y% on the price of L

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There was a series of two successive discounts of y% on the price of L  [#permalink]

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New post 05 Mar 2019, 23:08
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A
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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%
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Re: There was a series of two successive discounts of y% on the price of L  [#permalink]

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New post 07 Mar 2019, 04:37
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Top Contributor
Hello,

Greetings for the day!

This is a simple question which can be solved by assuming $100 as the price of the laptop and working backwards to obtain the final price of the laptop as $64.
Since we have to calculate the value of ‘y’, the options should naturally reflect this.

Clearly, options D and E cannot be the answers.

1 discount of 82% will take the price of the laptop much below $64, then where is the question of applying another 82% and getting $64.

A similar thing happens with option D. 36% of 100 is 36. Hence, after the first discount itself, the price reduces to $64. Now, if we apply another 36% discount, the price will not stay at $64, right?

So, options D and E are out of our way.

Now, out of the remaining options, let us pick 20%, because, this is clearly an easy number to deal with, considering the price of the laptop we have assumed.
When we apply the first discount of 20%, 100 becomes 80. When we apply the second discount of 20%, 80 becomes 64. This is clearly what we wanted.

Hence, the answer option is B.

The best approach for answering such questions is a combination of two approaches – eliminate the choices which do not make any sense and subsequently back solve using the answer options provided.

When you are picking options using which to back solve, pick numbers which are easy to deal with. Remember, it’s not a challenge to pick the most difficult option and then work backwards.

Post script: Alternatively, you can use the formula for successive discounts which is [ -a –b + ab/100]%

Hope this helps!
Cheers.
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Re: There was a series of two successive discounts of y% on the price of L  [#permalink]

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New post 10 Mar 2019, 19:47
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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%


Let p = the original price of the laptop. We can create the equation:

p x (100- y)/100 x (100 - y)/100 = p x 64/100

(100 - y)^2/100^2 = 64/100

Multiplying both sides of the equation by 100^2, we have:

(100 - y)^2 = 64(100)

√[(100 - y)^2] = +/-√6400

100 - y = 80 or 100 - y = -80

y = 20 or y = 180

We ignore y = 180 because an item cannot be discounted more than 100%. Thus, y = 20.

Answer: B
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Re: There was a series of two successive discounts of y% on the price of L  [#permalink]

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New post 06 Mar 2019, 11:46
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%


Let us consider the discount per cent = x%
And the initial price be 100
Hence the discounted price is 64

=> 100 * (1-(x/100))^2 = 64
=> (1-(x/100)) = 64/100= 8/10
=> x/100 = 1-(8/10) = 2/10
=> x = 20%

Hence B is the correct answer.
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Re: There was a series of two successive discounts of y% on the price of L  [#permalink]

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New post 07 Mar 2019, 07:12
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 know that two successive percentage changes of a% and b% are given by the formula: a + b + ab/100
This is discussed here: https://www.veritasprep.com/blog/2011/0 ... e-changes/

Total percentage change = - y - y + y^2/100 = -36% (since the final price of the laptop is 64% of original)

Note that if y were 18%, the total discount would have been less than 2*18% = 36% due to the impact of the y^2/100 term.

So the value of y must be greater than 18%. 20% seems about right since y^2 term will have a small impact. Let's check.

-20 - 20 + (-20*-20)/100 = -36%

Answer (B)
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Re: There was a series of two successive discounts of y% on the price of L  [#permalink]

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New post 21 Apr 2019, 16:02
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%



Discounted price = 64%

Discount after 2 successive discounts = 100 - 64 = 46.

Let the price of the laptop be 100.

value of y is given as answer choices.

Option B) 20%

1st discount = 100 * 20% =20

2nd discount = 80 * 20% = 16

20 + 16 = 46 ( total discount )

Thus B is the correct answer.
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There was a series of two successive discounts of y% on the price of L  [#permalink]

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New post 22 Apr 2019, 08:36
KSBGC wrote:
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%

Discounted price = 64%

Discount after 2 successive discounts = 100 - 64 = 46.

Let the price of the laptop be 100.

value of y is given as answer choices.

Option B) 20%

1st discount = 100 * 20% =20

2nd discount = 80 * 20% = 16

20 + 16 = 46 ( total discount )

Thus B is the correct answer.

KSBGC , your post has two typos. I think that you mean 36, not 46. :)
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Re: There was a series of two successive discounts of y% on the price of L  [#permalink]

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New post 22 Apr 2019, 18:35
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 price
C) 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 price

We 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 price
B) y = 20%

20% of $100 = $20 = ONE y discount in dollars
New price: ($100 - $20) = $80

• Stage 2 discount and changed price

20% 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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Re: There was a series of two successive discounts of y% on the price of L   [#permalink] 22 Apr 2019, 18:35
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