Weeks taken for calorie to fall below half of curr. level

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gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Fri May 02, 2014 10:17 pm

Hello,

I am unable to solve the following. Can you please help?

Jeff plans to lose weight by reducing his daily calorie intake each week. How many weeks does it take for his calorie intake to fall below half of its original level?

1.Jeff currently consumes 2,500 calories per day.
2.Jeff plans to reduce his daily calorie intake by 10 percent each week.

OA: B

I tried solving as follows:

Let Jeff's daily calorie intake be x
Hence his current weekly intake is 7x

We need to find out how many weeks it will take for his weekly intake to fall below 7x/2

1) x = 2500
=> Jeff's current weekly intake = 7x = 17500
We need to find out how many weeks it will take for his weekly intake to fall below 17500/2

- In-suff.

2) Jeff's planned reduced calorie intake per week = 6.3x

However, I was stuck beyond this point. Can you please help? Thanks a lot.

Best Regards,
Sri

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Source: Beat The GMAT — Data Sufficiency | Fri May 02, 2014 10:17 pm

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Fri May 02, 2014 10:34 pm

gmattesttaker2 wrote:Hello,

I am unable to solve the following. Can you please help?

Jeff plans to lose weight by reducing his daily calorie intake each week. How many weeks does it take for his calorie intake to fall below half of its original level?

1.Jeff currently consumes 2,500 calories per day.
2.Jeff plans to reduce his daily calorie intake by 10 percent each week.

OA: B

I tried solving as follows:

Let Jeff's daily calorie intake be x
Hence his current weekly intake is 7x

We need to find out how many weeks it will take for his weekly intake to fall below 7x/2

1) x = 2500
=> Jeff's current weekly intake = 7x = 17500
We need to find out how many weeks it will take for his weekly intake to fall below 17500/2

- In-suff.

2) Jeff's planned reduced calorie intake per week = 6.3x

However, I was stuck beyond this point. Can you please help? Thanks a lot.

Best Regards,
Sri

Hi Sri,

Let's start from where you got stuck. If it takes n weeks to bring 7x down to below 7x/2 at the rate of 10% reduction per week, then

7x (0.9)^n < 7x/2 or 7 (0.9)^n < 7/2 or n can be found out somehow. Hence it's sufficient!

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001

www.manyagroup.com

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