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# A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. On

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A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. On [#permalink]

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29 Oct 2017, 01:20
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A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. One year later, a share increased to Q dollars. The fraction by which the cost of a share of stock has increased in the year is

A. (Q - D)/D

B. (D - Q)/Q

C. D/Q

D. Q/D

E. (Q - D)/Q
[Reveal] Spoiler: OA

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A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. On [#permalink]

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29 Oct 2017, 12:22
Bunuel wrote:
A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. One year later, a share increased to Q dollars. The fraction by which the cost of a share of stock has increased in the year is

A. (Q - D)/D

B. (D - Q)/Q

C. D/Q

D. Q/D

E. (Q - D)/Q

Use the first part of percent increase formula-IMO, faster

The fraction by which the price of the stock increased can be calculated with percent change / percent increase formula, except without the (* 100).

The (* 100) changes the very fraction we seek into a percent.

Percent increase:

$$\frac{(New-Old)}{Old} * 100$$. Omit the * 100

Fractional increase where D is old price and Q is new price:

$$\frac{(New-Old)}{Old}=\frac{(Q - D)}{D}$$

Choose values

Let D dollars = 10
Let Q dollars = 15

The absolute increase in cost is 15 - 10 = 5 dollars.

5 is what fraction of original cost, 10?

$$\frac{part}{whole}=\frac{5}{10}=\frac{1}{2}$$

With D = 10, Q = 15, find the answer that yields result of $$\frac{1}{2}$$

Eliminate C and D immediately (with these numbers). The relationship between 10 and 15, regardless of which is the numerator and which is the denominator, is not 1/2

A. (Q - D)/D

$$\frac{(15 - 10)}{10}=(\frac{5}{10})=\frac{1}{2}$$ MATCH

B. (D - Q)/Q

$$\frac{(10 - 15)}{15}=$$ STOP. This result is negative. Indicates decrease. Prompt says increase. REJECT

E. (Q - D)/Q

$$\frac{(15-10)}{15}=(\frac{5}{15})=\frac{1}{3}$$. NO MATCH

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Re: A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. On [#permalink]

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29 Oct 2017, 18:51
$$\frac{Change}{Initial value}$$

$$\frac{(Q-D)}{D}$$

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Re: A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. On [#permalink]

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29 Oct 2017, 19:34
To find fractions it is always (New value - Original Value ) / Original Value

If the numerator is positive then there is a increase, if it is negative there is a decrease.

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Re: A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. On [#permalink]

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31 Oct 2017, 16:35
Bunuel wrote:
A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. One year later, a share increased to Q dollars. The fraction by which the cost of a share of stock has increased in the year is

A. (Q - D)/D

B. (D - Q)/Q

C. D/Q

D. Q/D

E. (Q - D)/Q

Recall that the formula (New - Old)/Old x 100 is used to calculate the percentage increase (or decrease). Without the “x 100” part, the formula (New - Old)/Old can be used to calculate the fraction increase (or decrease). Thus, the fraction by which the cost of a share of stock has increased in the year is:

(Q - D)/D

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Re: A share of stock in Ace Enterprises cost D dollars on Jan. 1, 1999. On   [#permalink] 31 Oct 2017, 16:35
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