Data Sufficiency

Hey all,

Q. Is 5^k less than 1,000 ?
(1) 5^(k-1)> 3000
(2) 5^(k-1)=(5^k)- 500

I solved the question and found the answer as D. But the correct answer is B. I am confused. Please help me out.

Prashant

killer1387 wrote:Hey all,

Q. Is 5^k less than 1,000 ?
(1) 5^(k-1)> 3000
(2) 5^(k-1)=(5^k)- 500

I solved the question and found the answer as D. But the correct answer is B. I am confused. Please help me out.

Prashant

Hi Prashant,

are you sure that you've posted (1) correctly? In its current form, (1) is definitely sufficient.

Algebraically:

5^(k-1)> 3000

multiplying both sides by 5:

5^(k-1) * 5^1 > 15000

5^(k-1+1) > 15000

5^k > 15000

and if 5^k is more than 15000, it's definitely NOT less than 1000.

Also, solving (2):

5^(k-1)=(5^k)- 500

500 = 5^k - 5^(k-1)

500 = 5(5^(k-1)) - 1(5^(k-1))

500 = (5-1)(5^(k-1)

500 = 4((5^(k-1))

125 = 5^(k-1)

5^3 = 5^(k-1)

3 = k-1
4 = k

so 5^k = 625

Is 625<1000? YES.

Since (1) appears to give us a definite "no" and (2) gives us a definite "yes", the question is fundamentally flawed (on the real GMAT you'll never get contradictory answers to the question).

If (1) read:

(1) 5^(k-1)< 3000

then (B) would be correct and the question would be legitimate.

What's the source?

killer1387 wrote:Hey all,

Q. Is 5^k less than 1,000 ?
(1) 5^(k-1)> 3000
(2) 5^(k-1)=(5^k)- 500

I solved the question and found the answer as D. But the correct answer is B. I am confused. Please help me out.

Prashant

hi i too believe answer should be D ...!!! if the answer is B.. than there might be two possible scenarios, either the given information in the question is not correct, or the answer key is wrong..!!!

Answer should be B if 5^k > 1000? (if 5^k < 1000 then D is the answer)

1) 5^k > 600 -> Insufficient
2) 5^k = 625 -> Sufficient

Thanx for the reply,

This question is from a question bank named 1000 DS which a friend of mine suggested for DS practice. This question confused me becoz of the contradictory answers i got from the two statements, in addition, the answer was also different, than what i obtained, in the key.

Prashant.

Hey,

Q. If a certain grove consists of 36 pecan trees, what was the yield per tree last year?
(1) The yield per tree for the 18 trees in the northern half of the grove was 60 kilograms last year.
(2) The yield per tree for the 18 trees in the eastern half of the grove was 55 kilograms last year.

(Question from 1000DS Section 16 Qusetion 7; Answer as per key: 'E', Doubt: Why 'C' is not correct)

Q. Is the number x between 0.2 and 0.7 ?

(1) 560x < 280
(2) 700x > 280
(Question from 1000DS Section 15 Qusetion 11; Answer as per key: 'C', Doubt: Why 'E' is not correct)

Suggest ur opinions please.

Prashant

Is the number x between 0.2 and 0.7 ?

(1) 560x < 280
x < 280/560
x < 28/56
x < 14/28
x < 1/2
x < 0.5 -> Not Sufficient

(2) 700x > 280
x > 280/700
x > 28/70
x > 14/35
x > 2/5
x > (1/5) * 2
x > 0.2 * 2
x > 0.4 -> Not sufficient

(3) Combined 0.4 < x < 0.5 is sufficient to answer. The answer to the question should be YES (the number x IS between 0.2 and 0.7). Correct answer is (C)