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Math Expert V
Joined: 02 Sep 2009
Posts: 58311
Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 63% (02:31) correct 37% (03:02) wrong based on 43 sessions

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Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

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Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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Bunuel wrote:
Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

given
m=1.2s
s=0.6D
m+s+d=23.2
solve we get s=6 so m= 7.2
next birthday m = 8
IMO B
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Joined: 25 Jun 2017
Posts: 34
GMAT 1: 660 Q45 V36 GPA: 3.5
WE: Human Resources (Consumer Products)
Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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Bunuel wrote:
Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

The answer should be B.

Given: $$M=\frac{6}{5}S$$ and $$S=\frac{3}{5}D$$ and M+S+D=23.2. We are looking for M+1=?

With three equations and 3 formulas, we can plug in and solve.

M+S+D=23.2

$$\frac{6}{5}S$$+S+$$\frac{5}{3}S$$=23.2

Solving for S:
Convert the fractions to a common denominator:

$$\frac{18}{15}S$$+$$\frac{15}{15S}$$+$$\frac{25}{15}S$$=23.2

$$\frac{58}{15}S$$=23.2

S=6

$$M=\frac{6}{5}*6$$

$$M=\frac{36}{5}$$

= 7.2

Therefore, M+1 = 8.2. Answer B.
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Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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Bunuel wrote:
Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

$$Mary = 1.2S$$

$$Sally = .6D$$

Rearrange $$S=.6D$$ to make.... $$Danielle=\frac{S}{.6}$$

$$M+D+S = 23.2$$

$$1.2S+\frac{S}{.6}+S=23.2$$

$$2.2S+\frac{S}{.6}=23.2$$ <--- (multiple each side by .6)

$$1.32S+S=13.92$$

$$2.32S=13.92$$

$$Sally=6$$

$$M=1.2S$$

$$M=1.2(6)$$

$$Mary=7.2$$ <--- Current Age
$$Mary=8$$ <--- Next Birthday
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Joined: 14 Oct 2015
Posts: 8040
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Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.  [#permalink]

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Bunuel wrote:
Mary is 20% older than Sally, and Sally is 40% younger than Danielle. The sum of their ages is 23.2 years. How old will Mary be on her next birthday?

(A) 7
(B) 8
(C) 9
(D) 10
(E) 11

We can let Danielle’s age = d, Sally’s age = 0.6d, and Mary’s age = 1.2 x 0.6d = 0.72d.

Since the sum of their ages is 23.2, we have:

d + 0.6d + 0.72d = 23.2

2.32d = 23.2

d = 10

So Mary is 0.72 x 10 = 7.2 years old, so she’ll be 8 on her next birthday.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: Mary is 20% older than Sally, and Sally is 40% younger than Danielle.   [#permalink] 27 Mar 2019, 18:58
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