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Kwasi has S dollars. The purchase price of a television set that Kwasi

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Bunuel
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Kwasi has S dollars. The purchase price of a television set that Kwasi [#permalink] New post   12 Apr 2018, 21:47
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Kwasi has S dollars. The purchase price of a television set that Kwasi wants to buy is P dollars plus 8 percent sales tax. Does Kwasi have enough money to purchase the item?

(1) P dollars = $405
(2) P dollars = 0.9S dollars
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Kwasi has S dollars. The purchase price of a television set that Kwasi [#permalink] New post   12 Apr 2018, 22:22
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Bunuel wrote:
Kwasi has S dollars. The purchase price of a television set that Kwasi wants to buy is P dollars plus 8 percent sales tax. Does Kwasi have enough money to purchase the item?

(1) P dollars = $405
(2) P dollars = 0.9S dollars


Question : Is S ≥ 1.08P ?

Statement 1: P dollars = $405

No information about S hence

NOT SUFFICIENT

Statement 2: P dollars = 0.9S dollars

i.e. S = 1.11 P

i.e. S is greater than 1.08 P

Exact relation between P and S hence

SUFFICIENT

Answer: option B
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Re: Kwasi has S dollars. The purchase price of a television set that Kwasi [#permalink] New post   12 Apr 2018, 22:25
Bunuel wrote:
Kwasi has S dollars. The purchase price of a television set that Kwasi wants to buy is P dollars plus 8 percent sales tax. Does Kwasi have enough money to purchase the item?

(1) P dollars = $405
(2) P dollars = 0.9S dollars


(1) P = $405, now lets apply 8% tax which is 8/100 * 405 = 32.4
So total purchase price = 405 + 32.4 = $437.4
But without knowing the value of S, we cannot say whether S is greater than equal to 437.4 or not. So not sufficient.

(2) P = 0.9*S. Now sales tax = 8% of 0.9S = 0.08*0.9*S = 0.072*S
So total purchase price = 0.9*S + 0.072*S = 0.972*S
But Kwasi has S dollars, which is definitely more than 0.972*S. Thus she has enough money. Sufficient.

Hence B answer
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Re: Kwasi has S dollars. The purchase price of a television set that Kwasi [#permalink] New post   13 Apr 2018, 00:11
Bunuel wrote:
Kwasi has S dollars. The purchase price of a television set that Kwasi wants to buy is P dollars plus 8 percent sales tax. Does Kwasi have enough money to purchase the item?

(1) P dollars = $405
(2) P dollars = 0.9S dollars


In this question there are 2 variables and sales tax % is given. We are to find out whether Kwasi has sufficient balance to buy a television set.

statement 1: only the value of p is given. P is basically the price of television set. Not sufficient. Kwasi may have that value or may not have. no information about S dollars belons to kwasi.

statement 2: It states that p is 90% of S. whatever value Kwasi has is 90% of the that amount is p. we know there will be 8% sales tax. So, tax will be 0.9*0.08= 0.072 dollar.
So, this statement is sufficient. The amount kwasi has is enough to buy a television set.

Thus, statement B is the answer.
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Re: Kwasi has S dollars. The purchase price of a television set that Kwasi [#permalink] New post   27 Apr 2018, 09:29
We want to estimate P + (8/100)S

I) value of S is unknown

II)P=0.9S
So value becomes 0.98S which is less than S
Hence B sufficient

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Re: Kwasi has S dollars. The purchase price of a television set that Kwasi [#permalink]
27 Apr 2018, 09:29
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