Charles the dog weighs 120 pounds

[BTGmoderatorDC]

Charles the dog weighs 120 pounds. 3 months from now, will Charles weigh over 220 pounds?

(1) Every month, Charles' weight increases by a different percentage ranging between 10% and 40%, inclusive.
(2) The monthly percent increase in Charles' weight is always divisible by 10.

What's the best way to determine whether statement 1 is sufficient?

OA E

[Brent@GMATPrepNow]

Charles the dog weighs 120 pounds. 3 months from now, will Charles weigh over 220 pounds?

(1) Every month, Charles' weight increases by a different percentage ranging between 10% and 40%, inclusive.
(2) The monthly percent increase in Charles' weight is always divisible by 10.

Target question: 3 months from now, will Charles weigh over 220 pounds?

Given: Charles PRESENTLY weighs 120 pounds

Statement 1: Every month, Charles' weight increases by a different percentage ranging between 10% and 40%, inclusive.
Let's test the two EXTREME values.
Case a: Charles' weight increases 10% each month
After 1 month: Charles' weight = (1.10)(120) = 132
After 2 months: Charles' weight = (1.10)(132) ≈ 145
After 3 months: Charles' weight = (1.10)(145) = a number that is wayyyy less than 220
In this case, the answer to the target question is NO, Charles does NOT weigh over 220 pounds

Case b: Charles' weight increases 40% each month
After 1 month: Charles' weight = (1.40)(120) = 168
After 2 months: Charles' weight = (1.40)(168) ≈ 220+
Since we're already over 220 pounds, we can stop calculating
In this case, the answer to the target question is YES, Charles DOES weigh over 220 pounds
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The monthly percent increase in Charles' weight is always divisible by 10.
IMPORTANT: Notice that the percent increases we tested in statement 1 were both divisible by 10
So, we can use the EXACT SAME values to show that statement 2 is also NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient.
So, the same counter-examples will also satisfy the two statements COMBINED.
So, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

[Jay@ManhattanReview]

Charles the dog weighs 120 pounds. 3 months from now, will Charles weigh over 220 pounds?

(1) Every month, Charles' weight increases by a different percentage ranging between 10% and 40%, inclusive.
(2) The monthly percent increase in Charles' weight is always divisible by 10.

What's the best way to determine whether statement 1 is sufficient?

OA E

We have to determine whether 3 months from now Charles will weigh over 220 pounds.

(1) Every month, Charles' weight increases by a different percentage ranging between 10% and 40%, inclusive.

Case 1: Take minimum possible values. Say the three different percentage ranging between 10% and 40% are 10%, 11%, and 12%.

Weight after one month = 120 + 10% of 120 = 120 + 12 = 132.
Weight after two months = 132 + 11% of 132 = 132 + ~10% of 132 = 132 + ~13 = ~145.
Weight after three months = ~145 + 12% of ~145 = ~145 + ~10% of 145 = ~145 + ~15 = ~160 << 220. The answer is No.

Case 2: Take maximum possible values. Say the three different percentage ranging between 10% and 40% are 38%, 39%, and 40%.

Weight after one month = 120 + ~40% of 120 = 120 + ~48 = ~170.
Weight after two months = ~170 + ~40% of 170 = ~170 + ~52 = ~222 > 220. There is no need to compute further. The answer is Yes.

No unique answer.

(2) The monthly percent increase in Charles' weight is always divisible by 10.

Cases discussed above are applicable here too. For Case 1, we can take rate of increase = 10% each and that for Case 2 = 40%.

No unique answer.

(1) and (2) combined

Case 1: Take three minimum possible values: 10%, 20% and 30% (Different and divisible by 10).

Weight after one month = 120 + 10% of 120 = 120 + 12 = 132.
Weight after two months = 132 + 20% of 132 = 132 + ~26 = ~160.
Weight after three months = ~160 + 30% of ~160 = ~160 + ~50 = ~210 < 220.

Note that we have approximated the values on the higher side, still, the final weight (~210) is less than 220. The answer is No.

Case 2: Take three maximum possible values: 20%, 30% and 40% (Different and divisible by 10).

There is no need to compute; since in Case 1, when the 10% will replace 40%, we will get much greater final value than 220. The answer would then be Yes.

We cannot get the unique answer. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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