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# If Sara were 1/4 of her current age, she would be fourteen years young

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Math Expert
Joined: 02 Sep 2009
Posts: 62499
If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 00:19
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5% (low)

Question Stats:

93% (01:45) correct 7% (01:17) wrong based on 44 sessions

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If Sara were 1/4 of her current age, she would be fourteen years younger than her brother Daniel. Daniel is twenty-two years younger than Sara. How old is Sara?

A. 36
B. 40
C. 44
D. 48
E. 52

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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 00:39
1
1
If Sara were 1/4 of her current age, she would be fourteen years younger than her brother Daniel. Daniel is twenty-two years younger than Sara. How old is Sara?

let Sara's current age= S

1/4*S=D-14

D=S-22

1/4*S=S-22-14

1/4*S=S-36

36=3/4*S

S=48 OPTION D
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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 00:48
1
If Sara were 1/4 of her current age, she would be fourteen years younger than her brother Daniel. Daniel is twenty-two years younger than Sara. How old is Sara?

Lets take sara current age=x
danieal current age=y
Given:
Eq1. x/4=y-14
Eq2. x=y+22
Solving for x&y. We get x=48, y=26. Ans D
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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 00:55
1
Let the present age of Sara = s and that of Daniel = d

If Sara were 1/4 of her current age, she would be fourteen years younger than her brother Daniel
—> s/4 = d - 14
—> d = s/4 + 14 ........ (1)

Daniel is twenty-two years younger than Sara
—> d = s - 22 ....... (2)

From (1) & (2),
—> s/4 + 14 = s - 22
—> 3s/4 = 36
—> s = 36*4/3 = 48

IMO Option D

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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 01:22
1
let S = x
given
x/4 = D-14
and D= x-22
x/4 = x-36
x= 48
IMO D
If Sara were 1/4 of her current age, she would be fourteen years younger than her brother Daniel. Daniel is twenty-two years younger than Sara. How old is Sara?

A. 36
B. 40
C. 44
D. 48
E. 52
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Schools: Ross '22, ISB '20, NUS '20
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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 02:28
1
s be sara present age
d be Daniel present age
d=s-22

s/4 = d-14
s/4 = s-22-14
s=48

OA:D

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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 03:17
1
Quote:
If Sara were 1/4 of her current age, she would be fourteen years younger than her brother Daniel. Daniel is twenty-two years younger than Sara. How old is Sara?

A. 36
B. 40
C. 44
D. 48
E. 52

D=S-22;
S/4=D-14;
S/4=S-22-14;
3S=4(36)…S=4(12)=48

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Posts: 788
Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 08:56
1
s-22=s/4 + 14
3s/4=36
s=4*36/3 =48

This implies Sarah is 48 years old.

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Posts: 598
Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 09:25
1
If Sara were 1/4 of her current age, she would be fourteen years younger than her brother Daniel. Daniel is twenty-two years younger than Sara. How old is Sara?

Daniel's current age = x
Sara's current age = y
x = y-22 -----1)

y/4 = x - 14, y = 4x-56-----2)
Put x into above equation to find y.
y = 4y-88-56
3y =144
y=48.

Imo. D
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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 09:48
1
If Sara were 1/4 of her current age, she would be fourteen years younger than her brother Daniel. Daniel is twenty-two years younger than Sara. How old is Sara?

A. 36
B. 40
C. 44
D. 48
E. 52

Let current age of Sara = x years
Current age of Daniel = x - 22 years

Now $$\frac{x}{4} = x - 22 - 14$$
x = 4x -36 * 4
x = 48

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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 10:02
1
(1/4)*S= D—14
D= S —22
—>( 1/4)S= S —22–14= S —36
36= S—(1/4)S=( 3/4)S
(3/4)S= 36
—> S = 36*(4/3)= 48

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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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06 Nov 2019, 10:32

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Re: If Sara were 1/4 of her current age, she would be fourteen years young  [#permalink]

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07 Nov 2019, 19:52
Let, Sara’s present age=4x
( 1/4*4x=x and since Sarah is younger than Daniel, Daniel Must be older than Sara)
So, Daniel’s age=x+14

Given, 4x-(x+14)=22
Or x= 12
Or 4x =48
So Sara’s present age=48.
Re: If Sara were 1/4 of her current age, she would be fourteen years young   [#permalink] 07 Nov 2019, 19:52
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