Gmat Prep (Arithmetic Sequence)?? Another Explanation....

[dferm]

NEED HELP....

[Ian Stewart]

Good problem, and tricky- not one I've seen before.

1) If a_1 is 24, we have no way to know how many terms are less than 10. If k is positive, none of the terms will be less than 10, but if k is -1000, all of the terms besides a_1 will be less than 10. Insufficient.

2) If a_8 is 10, and k is positive, all of the terms after a_8 will be greater than 10, and all the terms before a_8 will be less than 10. So we would have 7 terms which are smaller than 10 (a_1 through a_7). If k is negative, the reverse will be true: all the terms after a_8 will be less than 10, and all the terms before a_8 will be greater than 10. Again, 7 terms are smaller than 10 (a_9 through a_15). So sufficient.

B.

[Ian Stewart]

Just to add to my last post, if a is some term in the middle of the sequence, the terms before it and after it would be:

... a - 2k, a - k, a, a + k, a + 2k, ...

It's useful to note that this sequence is either constantly increasing (if k is positive) or constantly decreasing (if k is negative), which is what I was using in my solution above (in math-speak, the sequence is called 'strictly monotonic', but you don't need to know that term for the GMAT).

[anju]

Good problem, and tricky- not one I've seen before.

1) If a_1 is 24, we have no way to know how many terms are less than 10. If k is positive, none of the terms will be less than 10, but if k is -1000, all of the terms besides a_1 will be less than 10. Insufficient.

2) If a_8 is 10, and k is positive, all of the terms after a_8 will be greater than 10, and all the terms before a_8 will be less than 10. So we would have 7 terms which are smaller than 10 (a_1 through a_7). If k is negative, the reverse will be true: all the terms after a_8 will be less than 10, and all the terms before a_8 will be greater than 10. Again, 7 terms are smaller than 10 (a_9 through a_15). So sufficient.

B.

Hi Stuart,
isn't the question asking about the number of terms in the sequence greater than 10. As per your explanation, we cannot have a value of terms which are greater than 10.
Let me know if i misunderstood your explanation.
Thnx

[Ian Stewart]

Hi Stuart,
isn't the question asking about the number of terms in the sequence greater than 10. As per your explanation, we cannot have a value of terms which are greater than 10.
Let me know if i misunderstood your explanation.
Thnx

Stuart is another expert on this forum, but I assume your question is directed to me. I'm afraid I don't understand your question, however. As described above, if you know that a_8 is 10, you know that exactly seven terms are larger than 10, and exactly seven terms are smaller than 10.

[NIXBTG]

hi Stuart - Should't the choices be consistent..

According to your explanation everything before a8 in the sequence is less than 10, however according the choice 1 of the question a1 = 21, which conflicts your explanation.

Also. it may be a stupid question, but i'm gonna ask.. can the series start from a with a large postive number and progressively reduce i.e. 24,22,20...10.... How can you assume that all terms before a8 are less than 10??

Thanks

nix

[Testluv]

I also discussed this question here: https://www.beatthegmat.com/terms-in-a-s ... tml#206551

hi Stuart - Should't the choices be consistent..

According to your explanation everything before a8 in the sequence is less than 10, however according the choice 1 of the question a1 = 21, which conflicts your explanation.

Also. it may be a stupid question, but i'm gonna ask.. can the series start from a with a large postive number and progressively reduce i.e. 24,22,20...10.... How can you assume that all terms before a8 are less than 10??

Thanks

nix

I am neither Stuart nor Mr.Stewart, but when you are evaluating (2), you cannot refer to the info in (1); you have to pretend that (1) doesn't exist. You should evaluate the statements in combination only if each of (1) and (2) are insufficient by themselves.