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.
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Gmat Prep (Arithmetic Sequence)?? Another Explanation....
Source: Beat The GMAT — Data Sufficiency |
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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).
... 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).
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
ianstewartgmat.com
Hi Stuart,Ian Stewart wrote: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.
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
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Ian Stewart
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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.anju wrote: 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
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
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 also discussed this question here: https://www.beatthegmat.com/terms-in-a-s ... tml#206551
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.NIXBTG wrote: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
Kaplan Teacher in Toronto
