GMAT Data Sufficiency – The C-Trap 3

In one of the earliest Data Sufficiency posts on this blog, which you can read here and here, we discussed how the GMAT test-makers use the C-Trap to lure test-takers into making a mistake. The beauty of such questions is that the test-takers d not even realise that they have made a mistake. On the contrary they are very confident that they have answered it correctly.

The C-Trap is set to lull test-takers into thinking that they can easily get the answer by using both the statements. But while both statements together will give you the answer, the question you need to ask is whether both statements are in fact required. Remember you need to choose option (C) only if both statements ARE required.

The reason such questions foil test-takers has a lot to do with the mindset that they are in when approaching GMAT DS:

• they usually read the first statement and identify that the information they have is incomplete
• they then move into the second and the first thing they look for is information to complete the first statement!
• in the C-trap questions, the second statement will contain information that complements and completes the first statement
• so within no time it will seem as if that both together are required to give you the answer

But in reality one statement alone, usually the second one, will have enough information for you to answer the question!

Let us look at a GMAT Data Sufficiency question to understand this better.

In a sequence an = an-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

From the question we can deduce that this is an arithmetic progression that has 15 terms —  a1 to a15  with a common difference of k.

From the first statement we only get the value of the first term, a1 = 24. So from (1) alone we do not know how many terms are greater than 10. It depends on the value of the common difference k.

From the second statement, we know that the the eight term is 10. The eight term is nothing but the first term plus 7k, a1 + 7k = 10,  the formula for the same being  an = a + (n-1)d.

Then very quickly we realise that using both statements we can, get the value of k. Once we get the value of k, we can determine each term and count how many terms have a value greater than 10.

Since it is a DS question, it is not about calculating how many terms greater than 10 are there but only about determining if we have the information to do so, we quickly go ahead and mark (C) without a hint of a doubt that we might have answered this question incorrectly.

But whenever you are offered option (C) on a platter as it on this question — you should straight away be wary of it. While both statements together will give you the answer may be just one of the two statements would suffice!

There is another reason why you should closely evaluate statement (2) alone. It is giving you information that is directly related to the question asked. The question is asking you how many terms are greater than 10 and statement (2) is telling you that a8 = 10.

A closer examination will reveal that they have given you the the value of the middle-term of the 15 terms in the sequence, a8. There will be 7 terms after it — a9 to a15 — and seven terms before it — a1 to a7.  So there have to be 7 terms greater than 10 and 7 terms less than 10.

Depending upon the value of k, whether it is positive or negative, the terms greater than 10 will either be the first 7 terms or the last 7 terms. But that does not matter since all you asked to determine is how many terms are greater than 7.

I usually have people looking to re-take the GMAT after a first attempt preparing on their own, telling me — I do not know what happened, I thought I answered most of the Quant correctly, I did not find it very tough, but still I got only a 48!

I am sure they would have fell for a few C-Traps without even realising.

The GMAT Quant seems easy compared to Quant on Indian tests like the CAT but it is only deceptively so. The questions are designed in such a way that you cannot solve them in an auto-pilot mode; you have to be thinking on your feet all the time.

Go through the other two posts on the C-Trap and make sure you watch out for it while solving questions. Be careful not to become suspicious of every question where you get C as the answer. You should be wary only if you get C as the answer straightway without any effort whatsoever.

1. S Srinivasan says

Hello Mr.T ,
As ‘n’ is between 2 & 15 , there can be only 14 terms (incl both the ends). So in that case there will be two middle terms (a7,a8).

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2. When n=2 then a2 = a1 + k ..so there is a first term a1 as well…making it 15 terms from a1 to a15. It’s a different way of saying that it’s an AP of 15 terms.

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3. S Srinivasan says

Thanks for the Clarification…
I would request you to post in this blog on daily basis(like CAToholics) or alteast on alternative days.

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4. I wish I had the time to! Managing another CAT blog at imschennai.in as well. But will definitely be more regular.

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