A set has a series of numbers such as a that

Question

A set has a series of numbers such as a that  a_{n+2}= a_n + a_{n+1}  . What is the value of  a_7:a_5 ?

(1) The third term is 4
(2)  a_4: a_5 = 3:5

Source: 4gmat

alphonsa · Answer

Hi...

Sorry but I tried clicking on the M button to get the subscript.

But I wasn't able to post it.

desaichinmay22 · Answer

A set has a series of numbers such as a that a_(n+2)= a_(n) + a_(n+1) . What is the value of a_7:a_5?
1) The third term is 4
2) a_4: a_5 = 3:5

Statement 1 is insufficient. It is given that third term is 4. The value of fourth term depends on the value of third and second term. Since we don't know the value of second term, we can't determine further values of series.

Statement 2 :

a_4:a_5=3:5
a_4/(a_4+a_3)=3/5
5a_4=3(a_4+a_3)
5a_4=3a_4+3a_3
2a_4=3a_3
Therefore a_4 should be a multiple of 3 and a_3 should be a multiple of 2. Let us take the smallest multiples of 3 and 2.
Therefore value of a_3 can be 2 and value of a_4 can be 3. Since a_4=a_3+a_2
a_2=1 and a_1=1
Therefore series becomes : 1,1,2,3,5,8,13....
a_7:a_5=13:5

Statement 2 is sufficient.

Bunuel · Answer

A set has a series of numbers such as a that \(a_{n+2}= a_n + a_{n+1}\) . What is the value of \(a_7:a_5\)?

(1) The third term is 4. The 4th term is the sum of the previous two terms. If \(a_2=2\) and \(a_3=2\) you'll get one ratio for \(a_7:a_5\) but if \(a_2=1\) and \(a_3=3\) you'll get another ratio for \(a_7:a_5\). Not sufficient.

(2) \(a_4: a_5 = 3:5\) --> \(\frac{a_7}{a_5} = \frac{a_5+a_6}{a_5}=\frac{a_5+a_5+a_4}{a_5}=\frac{2*a_5+a_4}{a_5}=\frac{2*a_5}{a_5}+\frac{a_4}{a_5}=2+\frac{3}{5}\). Sufficient.

Answer: B.

P.S. You might find the following post helpful: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 (Writing Mathematical Formulas on the Forum)

Yadnesh · Answer

Hi Guys, This is my first post so please forgive me of all the formatting errors I am about to make

A set has a series of numbers such as a that \(a_{n+2}= a_n + a_{n+1}\) . What is the value of \(a_7:a_5\)?

(1) The third term is 4. The 4th term is the sum of the previous two terms. If \(a_2=2\) and \(a_3=2\) you'll get one ratio for \(a_7:a_5\) but if \(a_2=1\) and \(a_3=3\) you'll get another ratio for \(a_7:a_5\). Not sufficient.

(2) \(a_4: a_5 = 3:5\) --> \(\frac{a_7}{a_5} = \frac{a_5+a_6}{a_5}=\frac{a_5+a_5+a_4}{a_5}=\frac{2*a_5+a_4}{a_5}=\frac{2*a_5}{a_5}+\frac{a_4}{a_5}=2+\frac{3}{5}\). Sufficient.

Answer: B.

P.S. You might find the following post helpful: rules-for-posting-please-read-this-before-posting-133935.html#p1096628 (Writing Mathematical Formulas on the Forum)

I believe i need kudos to write mock tests so please help me about the same

Peace . BTW- Bunuel - Big fan of ur solutions. reminds me of pure mathematics

Bunuel · Answer

Welcome to the GMAT Club! To write math symbols you should use M button, check here: rules-for-posting-please-read-this-before-posting-133935.html#p1096628

bumpbot · Answer

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A set has a series of numbers such as a that

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