Data Sufficiency

Source : 800 Score Test Quant 1
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After the first term, each term in a sequence is five times greater than half the preceding term. If x is the first term of the sequence, and x does not equal zero, is the value of the fourth term minus the second term an integer?
(1) x is a multiple of 12.
(2) x is a multiple of 56.


OA : B

Query :
What does " five times greater than half the preceding term " mean ?

Does it mean Each term is 5/2 multiplied by the preceding term. If x is the first term, then the second term will be 5x/2

OR

6x/2 ??

I fail to understand this concept
Anyone Anyhelp !

an = (5/2)an_1 is correct.

the statement definetly means that the next term is 2.5 times the previous term. but i think looking at it that way makes it more complicated. i think the answer should be "b" because:

the difference between the 4th term and the 2nd term will be an integer if both the 4th and 2nd term are intgers. likewise, the next term in the sequence is only an integer if 1/2 of it is in integer. thus if x is a multiple of 12, the second term is a multiple of 6, the third term is a multiple of 3, and the fourth terms is a multiple of 1/2. if x has another factor of 2 in it (let's say its 24), the fourth term would be an integer. but if x does not have another factor of 2, (let's say it's 36), the fourth term is not an integer and the second one is. therefore, we don't have enough info, so we go to bce.

but with statement 2, 1st term is multiple of 56, 2nd term is multiple of 28, 3d term is multiple of 14 and 4th term is multiple of 7. since every multiple of 7 is an integer, we must have an integer minus an integer, so b alone is sufficient.

Thanks Stacey,

So my doubt ..with respect to this question was correct..!!
It indeed required an expert's say..
Thnks

Stacey Koprince wrote:Loose language.

If what they wanted to get us to do was: 5*(1/2)x

then it should have said: "five times half the preceding term."

Using "greater than" in there actually does change the meaning. If X is five times Y, then X = 5Y. If X is five times greater than Y, then X = Y + 5Y = 6Y.

What does the explanation indicate that they actually intended with this wording? If they intended 5*(1/2)x, then the wording is wrong and it's a bad question.

Source GMATPrep

When a tree was planted it was 4 feet. Its height increased by a constant amount each year for 6 years. After 6 years the tree was 1�5 taller than at the end of 4th year. By how many feet did the height of the tree increase each year?
a. 3�10
b. 2�5
c. 1�2
d. 2�3
e. 6�5

Here, 4+6x = 1/5 (4+4x) + (4+4x) RIGHT ???

Hi Stacey,


In here, if we interpret it as If X is five times greater than Y, then X > 5Y .. Is that correct?i.e it could be X=7Y, or 8Y or anythin and not necessarily 6Y
Moreover,since the question stem does not state that it has to be an integer..it can be any term.Is my understanding correct?

Stacey Koprince wrote:Loose language.

If what they wanted to get us to do was: 5*(1/2)x

then it should have said: "five times half the preceding term."

Using "greater than" in there actually does change the meaning. If X is five times Y, then X = 5Y. If X is five times greater than Y, then X = Y + 5Y = 6Y.

What does the explanation indicate that they actually intended with this wording? If they intended 5*(1/2)x, then the wording is wrong and it's a bad question.

mmslf75 wrote:

Stacey Koprince wrote:Loose language.

If what they wanted to get us to do was: 5*(1/2)x

then it should have said: "five times half the preceding term."

Using "greater than" in there actually does change the meaning. If X is five times Y, then X = 5Y. If X is five times greater than Y, then X = Y + 5Y = 6Y.

What does the explanation indicate that they actually intended with this wording? If they intended 5*(1/2)x, then the wording is wrong and it's a bad question.

Source GMATPrep

When a tree was planted it was 4 feet. Its height increased by a constant amount each year for 6 years. After 6 years the tree was 1�5 taller than at the end of 4th year. By how many feet did the height of the tree increase each year?
a. 3�10
b. 2�5
c. 1�2
d. 2�3
e. 6�5

Here, 4+6x = 1/5 (4+4x) + (4+4x) RIGHT ???

yet again, such a word problem
on..
https://www.beatthegmat.com/gmat-prep-qu ... tml#211245

Wording is not clear, but if we assume second term = 5/2 timesx, and so on

1st term = 5/2 x
2nd = 5/2*5/2x
...
4th = (5/2)^3 x
difference, 4th-2nd = 5/2x((5/2)^2-1) = x*5*21/8

Statement 1. x= 12m, now if x = 12 answer will be fraction and if x = 24 or more, then integer hence insufficient
Statement 2. X = 56m, answer will always be an integer as 56 is a multiple of 8 and hence suff.
Ans should be B in this case.