If the Sequence S has 100 terms what is the 83rd term

Question

If the Sequence S has 100 terms what is the 83 rd term

(1) Each term of S after the first term is 4 greater than the preceding term 
(2) The 84th term of S is twice the 82nd term

shrouded1 · Answer

(1)  a_n = a_1 + 4(n-1) 
Without knowing  a_1 , impossible to know  a_{83}

(2)  a_{84} = 2*a_{82} 
All we know is that  a_{83}  is the average of these two or  1.5 * a_{82} , but this is still enough to calculate it.

(1+2)  a_{84}=2*a_{82}  
 a_{84} = a_{82}+8 
 a_{82}+8=2*a_{82} 
 a_{82}=8 
 a_{83}=12

Sufficient

Answer is (C)

Bunuel · Answer

Question:  a_{83}=?

(1)  a_n=a_{n-1}+4 , for  n>1 . Not sufficient.

(2)  a_{84}=2*a_{82} . Not sufficient.

(1)+(2) From (1)  a_{84}=a_{83}+4  and  a_{83}-4=a_{82} , from (2):  a_{84}=2*a_{82}  -->  a_{83}+4=2*(a_{83}-4)  -->  a_{83}=12 . Sufficient.

Answer: C.

To elaborate more: 
(1) says that the sequence is an arithmetic progression and gives the value of common difference --> so we have a linear relationship between  any two terms . 
(2) provides us with  different  linear relationship between 2 particular terms.

(1)+(2) We have two distinct linear equations with two unknowns --> we can get missing value.

Hope it helps.

fronds · Answer

Took me about 8 minutes but I arrived at C once I realized I just had to see if I could work the information given into a solvable formula and then see which components I used to do so. This forum is proving very helpful already! Thanks all

GSBae · Answer

I solved this in 17 seconds once I realized the information given.

1) From the first statement, we realize we can write every term of the sequence in terms of  S_1 .  S_2 = S_1+4 ,  S_3 = S1 + 2(4)....S_{83} = S_1 + 82(4) . However, we still don't know  S_1 , so insufficient.

2) Clearly insufficient.

Together, we have a relationship between the two terms, both of which can be expressed in terms of  S_1 . That's one equation with one unknown. Therefore, we can easily solve for  S_1  and therefore  S_{83}. . Sufficient.

Answer: C

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

If the Sequence S has 100 terms what is the 83rd term

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If the Sequence S has 100 terms what is the 83rd term

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards