a1,a2,a3...a15
In the sequence shown, a(n) = a(n-1)+k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10?
(1) a1 = 24
(2) a8 = 10
Solution:
Note that k can be either positive or negative,
If k is positive, the sequence increases and if k is negative, sequence decreases.
Consider first (1) alone.
a1 = 24.
If k = 1, a2 = 25, a3 = 26,.......a15 = 38.
So all 15 terms are greater than 10.
Next let k = -10,
So a2 = 14, a3 = 4,.......
So only a1 and a2 or 2 terms are greater than 10.
Since nothing definite can be said (1) alone is not sufficient.
Next consider (2) alone.
a8 = 10.
Let k be positive.
Then a9= 10+k >10, a10 = 10+2k >10, .....a15 = 10 + 7k > 10.
So exactly 7 terms are > 10.
Next let k be negative.
So a7 = 10 - k > 10 because k is negative.
Similarly a6, a5, a4,.a1 are all greater than 10.
Again exactly 7 terms will be greater than 10.
So (2) alone is sufficient.
The correct answer is (B).
Sequence
This topic has expert replies
Source: Beat The GMAT — Data Sufficiency |
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Hey Rahul. I have totally understood the way you've attacked this question but there's one thing that's bothering me.Rahul@gurome wrote:a1,a2,a3...a15
In the sequence shown, a(n) = a(n-1)+k, where 2<=n<=15 and k is a nonzero constant. How many of the terms in the sequence are greater than 10?
(1) a1 = 24
(2) a8 = 10
Solution:
Note that k can be either positive or negative,
If k is positive, the sequence increases and if k is negative, sequence decreases.
Consider first (1) alone.
a1 = 24.
If k = 1, a2 = 25, a3 = 26,.......a15 = 38.
So all 15 terms are greater than 10.
Next let k = -10,
So a2 = 14, a3 = 4,.......
So only a1 and a2 or 2 terms are greater than 10.
Since nothing definite can be said (1) alone is not sufficient.
Next consider (2) alone.
a8 = 10.
Let k be positive.
Then a9= 10+k >10, a10 = 10+2k >10, .....a15 = 10 + 7k > 10.
So exactly 7 terms are > 10.
Next let k be negative.
So a7 = 10 - k > 10 because k is negative.
Similarly a6, a5, a4,.a1 are all greater than 10.
Again exactly 7 terms will be greater than 10.
So (2) alone is sufficient.
The correct answer is (B).
Why are we assuming k>-10 in cases where we've considered k to be negative.
In the second case, if k=-20, all the terms would be negative. How can we assume a7=10-k to be positive. K can be anything. Please Explain.
Thanks.
GMAT/MBA Expert
-
Rahul@gurome
- GMAT Instructor
- Posts: 1179
- Joined: Sun Apr 11, 2010 9:07 pm
- Location: Milpitas, CA
- Thanked: 447 times
- Followed by:88 members
We are nowhere assuming that k > -10 where k is negative.
By statement (2) a8 = 10.
Let k be negative such that k = -b where b is positive.
So a7 = 10 - (-b) = 10+b = 10 +( a positive quantity). Or a7 > 10.
a6 = a7 - k = a7 + b = 10+b+b = 10+2b = 10 + (a positive quantity). Or a6>10.
You can similarly deduce that a5, a4, a3, a2, a1 are all greater than 10 if k is negative
By statement (2) a8 = 10.
Let k be negative such that k = -b where b is positive.
So a7 = 10 - (-b) = 10+b = 10 +( a positive quantity). Or a7 > 10.
a6 = a7 - k = a7 + b = 10+b+b = 10+2b = 10 + (a positive quantity). Or a6>10.
You can similarly deduce that a5, a4, a3, a2, a1 are all greater than 10 if k is negative
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
