GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 24 Jun 2018, 04:04

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Hunter was one fifth as old as Erica, x years ago. In x years, Erica

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46305
Hunter was one fifth as old as Erica, x years ago. In x years, Erica [#permalink]

### Show Tags

17 Sep 2017, 03:24
00:00

Difficulty:

35% (medium)

Question Stats:

77% (02:25) correct 23% (02:53) wrong based on 48 sessions

### HideShow timer Statistics

Hunter was one fifth as old as Erica, x years ago. In x years, Erica will be twice as old as Hunter. What is the ratio of Hunter's current age to Erica's current age?

A. 11:15
B. 3:7
C. 5:13
D. 9:17
E. 7:23

_________________
BSchool Forum Moderator
Joined: 26 Feb 2016
Posts: 2839
Location: India
GPA: 3.12
Hunter was one fifth as old as Erica, x years ago. In x years, Erica [#permalink]

### Show Tags

17 Sep 2017, 07:24
Let age of Erica after x years be E and Hunter's age be H.

From questions stem, E = 2H

Also,$$H - 2x = \frac{1}{5}(E - 2x) => 5H - 10x = E - 2x$$

Substituting the value of E, we will get $$3H = 8x => \frac{H}{x}= \frac{8}{3}$$

If H = 8, E = 16
2x(6) years ago, Hunter's age is 2 and that is one-fifth the age of Erica!

Since, we are asked for their current ages, it must be (8-3:16-3) or 5:13(Option C)
_________________

You've got what it takes, but it will take everything you've got

Senior Manager
Joined: 02 Jul 2017
Posts: 294
GMAT 1: 730 Q50 V38
Hunter was one fifth as old as Erica, x years ago. In x years, Erica [#permalink]

### Show Tags

17 Sep 2017, 11:10
Hunter was one fifth as old as Erica, x years ago.
=> $$(H-x)= \frac{1}{5}(E-x)$$
=> $$5H-5x= E-x$$
=> $$5H =E+4x$$

In x years, Erica will be twice as old as Hunter.
=> $$2(H+x)= E+x$$
=> $$2H+2x=E+x$$
=> $$2H=E-x$$

What is the ratio of Hunter's current age to Erica's current age: $$\frac{H}{E}$$????

=>$$5H =E+4x$$
=> $$x= \frac{5H-E}{4}$$

as $$2H=E-x$$ => $$2H=E-\frac{5H-E}{4}$$ => $$13H =5E$$
$$\frac{H}{E} = \frac{5}{13}$$

SC Moderator
Joined: 22 May 2016
Posts: 1765
Hunter was one fifth as old as Erica, x years ago. In x years, Erica [#permalink]

### Show Tags

19 Sep 2017, 18:17
Bunuel wrote:
Hunter was one fifth as old as Erica, x years ago. In x years, Erica will be twice as old as Hunter. What is the ratio of Hunter's current age to Erica's current age?

A. 11:15
B. 3:7
C. 5:13
D. 9:17
E. 7:23

x years ago, Hunter was 1/5 as old as Erica

$$H - x = \frac{1}{5}(E - x)$$
$$5(H - x) = E - x$$
$$5H - 5x = E - x$$
$$5H = E + 4x$$ ······ (A)

In x years, Erica will be twice as old as Hunter

$$2(H + x) = E + x$$
$$2H + 2x = E + x$$
$$2H = E - x$$ ······· (B)

Looking at (A) and (B) . . . Multiply (B) by 4 (to eliminate x). Add it to (A).

$$8H = 4E - 4x$$
$$5H = E + 4x$$
----------------------
$$13H = 5E$$

Ratio of Hunter's current age to Erica's current age?

$$13H = 5E$$

$$\frac{H}{E} = \frac{5}{13}$$

_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

Hunter was one fifth as old as Erica, x years ago. In x years, Erica   [#permalink] 19 Sep 2017, 18:17
Display posts from previous: Sort by