Did the quantity of bacteria increase

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gmatdriller: Master | Next Rank: 500 Posts; Posts: 418; Joined: Sun Jul 04, 2010 12:48 pmFollowed by: 3 members; Thanked: 6 times

by gmatdriller » Sun Oct 28, 2012 12:27 am

Did the quantity of bacteria in an experiment increase by at least 15% from 1922 to 1937?
(1) The quantity of bacteria increased each year by the same percent each year from 1922 to 1937
(2) The quantity of bacteria increased by at most 1 percent each year from 1922 to 1937.

[spoiler](1) we could have 0.0001% or 100% each year.,,INSUFF
(2) Also either 0.00001, or 1% could be applicable...INSUFF
Combining:
I set up as follows: 100, 101, 102.. 103, 104 as minimum values each year; so yr 1937 should also give us at least 115(+xxx)...15yrs from 1922...
But using 0.0001% each yr will not yield 15%, so E.

However, y tried 1% (extreme) using Q(1.01)^14 ==> Q(1 + 0.01)^14
= 1^14 + 14C1(0.01) + 14C2 (0.01)^2 +14C3 (0.01)^3 +14C4(0.01)^4
1 + 0.14 + 0.0091 + 0.000504 +0.00000924 = 1.14961324
1.14961324 is still < 15%...this doesn't look an efficient method or am I missing something?

OA is E[/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Sun Oct 28, 2012 12:27 am

nisagl750: Master | Next Rank: 500 Posts; Posts: 145; Joined: Tue Jan 31, 2012 6:50 amFollowed by: 2 members; Location: New Delhi; Thanked: 16 times; GMAT Score:760

by nisagl750 » Thu Nov 29, 2012 11:35 pm

gmatdriller wrote:Did the quantity of bacteria in an experiment increase by at least 15% from 1922 to 1937?
(1) The quantity of bacteria increased each year by the same percent each year from 1922 to 1937
(2) The quantity of bacteria increased by at most 1 percent each year from 1922 to 1937.

[spoiler](1) we could have 0.0001% or 100% each year.,,INSUFF
(2) Also either 0.00001, or 1% could be applicable...INSUFF
Combining:
I set up as follows: 100, 101, 102.. 103, 104 as minimum values each year; so yr 1937 should also give us at least 115(+xxx)...15yrs from 1922...
But using 0.0001% each yr will not yield 15%, so E.

However, y tried 1% (extreme) using Q(1.01)^14 ==> Q(1 + 0.01)^14
= 1^14 + 14C1(0.01) + 14C2 (0.01)^2 +14C3 (0.01)^3 +14C4(0.01)^4
1 + 0.14 + 0.0091 + 0.000504 +0.00000924 = 1.14961324
1.14961324 is still < 15%...this doesn't look an efficient method or am I missing something?

OA is E[/spoiler]

Yes the answer is E
For second approach, shouldn't it be (1.01)^15 ??

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Fri Nov 30, 2012 8:55 am

gmatdriller wrote:Did the quantity of bacteria in an experiment increase by at least 15% from 1922 to 1937?
(1) The quantity of bacteria increased by the same percent each year from 1922 to 1937
(2) The quantity of bacteria increased by at most 1 percent each year from 1922 to 1937.

Target question: Did the quantity increase by at least 15% from 1922 to 1937?

Statement 1: The quantity of bacteria increased by the same percent each year from 1922 to 1937
To see why this statement is not sufficient, consider these two possible cases
Case a: The quantity increased by 0.00001% each year, in which case the percent increase from 1922 to 1937 is not at least 15%
Case b: The quantity increased by 1% each year, in which case the percent increase from 1922 to 1937 is at least 15%

ASIDE: If the quantity of bacteria increases 1% each year, then in the 15 years from 1922 to 1937, the overall increase will be greater than 15%. What the actual increase is doesn't matter, since the target question asks whether the increase was at least 15%, and we can be certain that it is at least 15%.

Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The quantity of bacteria increased by at most 1 percent each year from 1922 to 1937.
To see why this statement is not sufficient, consider these two possible cases
Case a: The quantity increased by 0.00001% each year, in which case the percent increase from 1922 to 1937 is not at least 15%
Case b: The quantity increased by 1% each year, in which case the percent increase from 1922 to 1937 is at least 15%
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
To see why the combined statements are not sufficient, consider these two possible cases
Case a: The quantity increased by 0.00001% each year, in which case the percent increase from 1922 to 1937 is not at least 15%
Case b: The quantity increased by 1% each year, in which case the percent increase from 1922 to 1937 is at least 15%
Since we still cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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