Jeff plans to lose weight by reducing his daily calorie intake each we

Hi 23a2012,

With certain DS questions, you have to pay careful attention to what is specifically ASKED for. The nature of the question might allow you more than one way to approach the work.

Here, we're asked how many weeks it will take Jeff to reduce his calorie intake by HALF.

Fact 1: Jeff currently consumes 2,500 calories per day.

This tells us nothing about how many calories he will reduce each week, so we cannot answer the question.
Fact 1 is INSUFFICIENT.

Fact 2: Jeff plans to reduce his daily calorie intake by 10 percent each week.

While we're not told Jeff's starting number of calories, THAT information is actually irrelevant here. We know that he's going to reduce his number of calories by 10% each week, so we COULD figure out how many weeks it takes to get that number down to HALF (meaning 50%). Here's how you could do the work, if you needed to...

By reducing the number by 10% each week, that is mathematically equivalent to multiplying the prior week's number by 0.9

Start = X
Week 1 = .9X
Week 2 = .9(.9X) = .81X
Week 3 = .9(.81X) = .729X
Week 4 = .9(.729X) = .6561X
Week 5 = .9(.6561X) = .59049X
Week 6 = .9(.59049X) = .531441X
Week 7 = .9(.531441X) = .4782969X

As you can see, the math IS rather tedious, but we don't actually have to do the math to answer this question. We know that we WOULD eventually get to the answer and THAT knowledge is enough.
Fact 2 is SUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich