Question: 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.

A) Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B) Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D) EACH statement ALONE is sufficient.
E) Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: B
Solution and Explanation:

Approach Solution 1:

When answering some DS questions, you need to pay close attention to what is ASKED for. Depending on how the question is worded, you might be able to do the work in more than one way.
Here, we are asked how many weeks it will take Jeff to cut his calorie intake by HALF.

Fact 1: Jeff eats 2,500 calories per day at the moment.
This doesn't tell us anything about how many calories he will cut each week, so we can't answer the question.
Fact 1 is not enough.

Jeff is going to cut his daily calorie intake by 10% every week.
We don't know how many calories Jeff had to start with, but that doesn't really matter. We know that he will cut his calories by 10% every week, so we can figure out how many weeks it will take to get that number down to 50%. If you had to, here's how you could do the work…
If you cut the number by 10% every week, that's the same as multiplying the number from the week before 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, math is boring, but we don't have to do math to answer this question. We knew that we would find the answer eventually, and that was enough.
Fact 2 is enough.
B is the correct answer.

Approach Solution 2:

One Statement Only:
At the moment, Jeff eats 2,500 calories every day.
Given that we are unsure of the extent of his planned calorie reduction, statement one is insufficient to provide a satisfactory response to the query.

Only Statement Two:
Every week, Jeff wants to cut 10% of his daily caloric consumption.
The second claim is adequate to respond to the query. For instance, if he consumed 2000 calories per day during the first week, 2000 x 0.9 = 1800 calories per day during the next week. In the third week, he consumes 1800 x 0.9 = 1620 calories per day. So, by carrying on with this method, we can determine how many weeks it takes for his calorie consumption to drop to half of what it was initially. (Note: We simply need to be aware that it's possible to find the precise number of weeks; we don't need to.)

B is the correct answer.

Approach Solution 3:

We must be aware of the calorie reductions in order to solve them.
According to statement 2, Jeff will cut back on his daily caloric consumption by 10% per week.
If week one is x, then week two is 0.9, week three is 0.81, and so on.

Statement 2 is sufficient because we can determine when his caloric intake is less than 0.5 times. We don't need to know the precise calorie amounts because the calorie reductions are done by a percentage.
His current consumption level is revealed in Statement 1, yet the number of calories consumed has decreased. Insufficient, hence choice B is the right response.
B is the correct answer.

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