Question: Find the Value of Term 10

Comment on Find the Value of Term 10

Hi Brent, wondering if on GMAT can we get a case where 2 statements may give different values of k and we say both are sufficient?

for example the above question itself if we get k=5 in statement 1 and k=10 in statement 2? Will the answer be still D?
gmat-admin's picture

If we solve the equation in statement 2, we get k = 5

Start with: 80k + 150 = 77k + 165
Subtract 150 from both sides: 80k = 77k + 15
Subtract 77k from both sides: 3k = 15
Solve: k = 5

A useful feature of Data Sufficiency questions is that the statements will never contradict each other.

So, for example, you will never find a question in which one statement says x = 3 and the other statement says x = 10

For more on this, watch: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1104

Cheers,
Brent

I'm confused as well since statement 2 only tells us the ratio but not the exact value
gmat-admin's picture

If statement 2 (term_8/term_7 = 11/10) were the only piece of information, then we wouldn't be able to determine the value of term_10.
However, the given information also tells us that term_n = kn + 15.

So, from term_2, we can conclude that k = 5 (see the calculations in my response about).
Once we know that k = 5, we can use the fact that term_n = kn + 15.
Replace n with 10 to get: term_10 = k(10) + 15.
Plug k = 5 into the above equation to get: term_10 = 5(10) + 15 = 50 + 15 = 65
Sufficient.

Does that help?

Wow, I immediately chose D after reading the question, im surprised I did it correctly, probably because these two statements can be solved too obviously!

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