In the Sequence F, the first term has the value seven and each success

Question

In the Sequence F, the first term has the value seven and each successive term is obtained by multiplying the previous term by the constant r. What is the value of r?

(1) The value of the fourteenth term of Sequence F is sixteen times the value of the twelfth term.

(2) The value of the fifteenth term of Sequence F is sixty-four times the value of the twelfth term.

This is a  Data Sufficiency Butler Question

Check the links to other Butler Projects: 
 
   Data Sufficiency Butler 
   Problem Solving Butler  
   Sentence Correction Butler  
   Reading Comprehension Butler  
   Integrated Reasoning Butler

zhanbo · Answer

The first term: 7
The 2nd term: 7 * r
The 3rd term: 7 * r^2
...
The nth term: 7 * r^(n-1)

(1) Only
14thTerm / 12thTerm = 16
So r^2 = 16
r can be 4 or -4
Insufficient.

(2) Only
15thTerm / 12thTerm = 64
So r^3=64
r must be 4
Sufficient.

The answer is thus  (B)

cosmicomet · Answer

Nowhere it is mentioned that r is non zero. That is why I thought E. Is this a valid point?

egmat · Answer

Hi cosmicomet,

This is a genuinely sharp DS instinct. You're right that the algebra in zhanbo's solution quietly  divides by `r^11` , and dividing by something that could be zero is exactly the kind of move worth challenging. So credit where it's due.

Here's why it still lands on  B , though.

Does `r = 0` even fit?  Plug it in: the  12th  term would be `7 · 0^11 = 0`, and the  15th  term `7 · 0^14 = 0`. Then "15th =  64  × 12th" reads `0 = 64 · 0` - technically true. So  mathematically  `r = 0` does satisfy the equation.

Why we don't count it.  The sequence is built by multiplying by a  constant ratio  `r` - that's a geometric sequence, and by standard convention its ratio is  nonzero . If `r = 0`, the sequence collapses to `7, 0, 0, 0, ...` and there's no real "ratio" left to speak of; the relationships become degenerate `0 = 0` identities that hold for  any  multiplier. The GMAT treats that as outside the intended setup.

So once `r = 0` is off the table:

- Statement ( 1 ): `r^2 = 16` → `r = 4`  or  `r = -4` →  not sufficient .
- Statement ( 2 ): `r^3 = 64` → `r = 4` only (one real cube root) →  sufficient .

That leaves  B . Keep that zero-check habit, though - most DS questions reward it; this one just defines it away.

Answer: B

In the Sequence F, the first term has the value seven and each success

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

In the Sequence F, the first term has the value seven and each success

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