GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2019, 05:30

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Arithmetic sequences S1 and S2 have 5 terms each. If the difference be

Author Message
Manager
Joined: 05 Oct 2016
Posts: 89
Location: United States (OH)
GPA: 3.58
Arithmetic sequences S1 and S2 have 5 terms each. If the difference be  [#permalink]

### Show Tags

26 Jan 2018, 12:40
1
00:00

Difficulty:

75% (hard)

Question Stats:

57% (02:51) correct 43% (02:44) wrong based on 23 sessions

### HideShow timer Statistics

Arithmetic sequences S1 and S2 have 5 terms each. If the difference between two consecutive terms of S2 is twice the difference between two consecutive terms of S1, what is the ratio of the fifth term of S1 and the fifth term of S2?

(1) The first term of S1 is twice the first term of S2

(2) The second term of both S1 and S2 is 3

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4471
Arithmetic sequences S1 and S2 have 5 terms each. If the difference be  [#permalink]

### Show Tags

26 Jan 2018, 17:41
SandhyAvinash wrote:
Arithmetic sequences S1 and S2 have 5 terms each. If the difference between two consecutive terms of S2 is twice the difference between two consecutive terms of S1, what is the ratio of the fifth term of S1 and the fifth term of S2?

(1) The first term of S1 is twice the first term of S2

(2) The second term of both S1 and S2 is 3

Dear SandhyAvinash,

I'm happy to respond.

To tell you the truth, I am little suspicious of this question, because I don't believe the GMAT expect students to recognize the term "arithmetic sequence" and understand its implications. An arithmetic sequence is one in which each term differs from the previous term by the addition of a fixed difference. If S1 has a fixed difference of d, then the prompt tells us that S2 has a fixed difference of 2d--these are the amounts added to get from one term to the next.

The starting values of the two sequences are unknown. The prompt tells us that the two sequences are of the form.

S1 = {a, a+d, a+2d, a+3d, a+4d}
S2 = {b, b+2d, b+4d, b+6d, b+8d}

Notice that there are three unknowns.

(1) The first term of S1 is twice the first term of S2

We are told a = 2b. This gives us one equation for three variables. We can't solve. The first statement, alone and by itself, is insufficient.

(2) The second term of both S1 and S2 is 3

a+d = 3
b + 2d = 3

This statement alone gives us two equation for three unknowns. We still can't solve. The second statement, alone and by itself, is insufficient.

Combined:
Now we have three equations:
a = 2b
a + d = 3
b + 2d = 3
Three equations for three unknowns. We can solve for everything. Combined, the statements are sufficient.

OA = (C)

It's not needed for the solution to the DS problem, but here's the solution:
Equation #1: a = 2b
Equation #2: a + d = 3
Equation #3: b + 2d = 3

Substitute equation #1 into equation #2 to eliminate a and get two equations for b and d.
2b + d = 3
Multiply this by two and subtract equation #3
(4b + 2d = 6)
-(b + 2d = 3)
3d = 3
d = 1

Substituting into equation #3, we get b = 1.
Substituting into equation #1 or #2, we get a = 2.

S1 = {2, 3, 4, 5, 6}
S2 = {1, 2, 5, 6, 9)

ratio requested = $$\tfrac{6}{9}$$ = $$\tfrac{2}{3}$$

Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager
Joined: 05 Oct 2016
Posts: 89
Location: United States (OH)
GPA: 3.58
Re: Arithmetic sequences S1 and S2 have 5 terms each. If the difference be  [#permalink]

### Show Tags

26 Jan 2018, 20:43
mikemcgarry wrote:
SandhyAvinash wrote:
Arithmetic sequences S1 and S2 have 5 terms each. If the difference between two consecutive terms of S2 is twice the difference between two consecutive terms of S1, what is the ratio of the fifth term of S1 and the fifth term of S2?

(1) The first term of S1 is twice the first term of S2

(2) The second term of both S1 and S2 is 3

Dear SandhyAvinash,

I'm happy to respond.

To tell you the truth, I am little suspicious of this question, because I don't believe the GMAT expect students to recognize the term "arithmetic sequence" and understand its implications. An arithmetic sequence is one in which each term differs from the previous term by the addition of a fixed difference. If S1 has a fixed difference of d, then the prompt tells us that S2 has a fixed difference of 2d--these are the amounts added to get from one term to the next.

The starting values of the two sequences are unknown. The prompt tells us that the two sequences are of the form.

S1 = {a, a+d, a+2d, a+3d, a+4d}
S2 = {b, b+2d, b+4d, b+6d, b+8d}

Notice that there are three unknowns.

(1) The first term of S1 is twice the first term of S2

We are told a = 2b. This gives us one equation for three variables. We can't solve. The first statement, alone and by itself, is insufficient.

(2) The second term of both S1 and S2 is 3

a+d = 3
b + 2d = 3

This statement alone gives us two equation for three unknowns. We still can't solve. The second statement, alone and by itself, is insufficient.

Combined:
Now we have three equations:
a = 2b
a + d = 3
b + 2d = 3
Three equations for three unknowns. We can solve for everything. Combined, the statements are sufficient.

OA = (C)

It's not needed for the solution to the DS problem, but here's the solution:
Equation #1: a = 2b
Equation #2: a + d = 3
Equation #3: b + 2d = 3

Substitute equation #1 into equation #2 to eliminate a and get two equations for b and d.
2b + d = 3
Multiply this by two and subtract equation #3
(4b + 2d = 6)
-(b + 2d = 3)
3d = 3
d = 1

Substituting into equation #3, we get b = 1.
Substituting into equation #1 or #2, we get a = 2.

S1 = {2, 3, 4, 5, 6}
S2 = {1, 2, 5, 6, 9)

ratio requested = $$\tfrac{6}{9}$$ = $$\tfrac{2}{3}$$

Does all this make sense?
Mike

Thanks a lot, Mike, your way of explaining things is fantastic

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Non-Human User
Joined: 09 Sep 2013
Posts: 13731
Re: Arithmetic sequences S1 and S2 have 5 terms each. If the difference be  [#permalink]

### Show Tags

28 Nov 2019, 01:05
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.
_________________
Re: Arithmetic sequences S1 and S2 have 5 terms each. If the difference be   [#permalink] 28 Nov 2019, 01:05
Display posts from previous: Sort by