Alan and Sue have each been saving one dollar a day and will continue

Assume 'x' days from today, Alan will save 1/2 as much as Sue.

Statement 1-
\((7+x)=\frac{1}{2}(27+x)\)
x=13

Sufficient

Statement 2-
Savings by Alan, as of today= A
Savings by Sue, as of today= S

\((A+3)=\frac{1}{3}(S+3)\)

Also, \((A+x)=\frac{1}{2}(S+x)\)

We have 2 equations and 3 unknowns (A, S and x)

Insufficient

OFFICIAL EXPLANATION:

Let A be the amount Alan has saved as of today. Let S be the amount Sue had already saved when Alan started saving. Then, as of today, Sue has saved S + A dollars. Determine d, the number of days from today that Alan will have saved half as much as Sue. That is, determine d, where A + d = 62604.png(S + A + d) or, after algebraic manipulation, determine d such that d = S − A.

 A) It is given that A = 7 and S = 27, so d = 20; SUFFICIENT.
 B) It is given that three days from today, Alan will have saved one-third as much as Sue, from which it follows that A + 3 = 62611.png(S + A + 3) or, after algebraic manipulation, S = 2A + 6. Then, d = S − A = (2A + 6) − A = A + 6. Since the value of A can vary, the value of d cannot be determined; NOT sufficient.
The correct answer is A;
statement 1 alone is sufficient.

Though I understood the solution but I had a question :-

what do we mean by one-half in the phrase in how many days from today will Alan have saved one-half as much as Sue?

one-half is 0.5 or 1.5 ?

(Although 0.5 is indeed logical as 1.5 would bring negative answer)
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It is to be interpreted as 0.5.
One-half means we have one "half"--> one "0.5"
Two-halves means we have two "halves"--> two "0.5" = 1

"1.5" would be said as "One and a half"

+1 Kudos if you like the explanation

Hi nick1816

OA explanation mentions d=20. even i think it should be 13. The answer takes S=27 as the time before Ala started saving.

Hi Bunuel,

Can you plz. confirm and check the correct value of d

Question: Alan and Sue have each been saving one dollar a day and will continue to do so for the next month. If Sue began saving several days before Alan, in how many days from today will Alan have saved one-half as much as Sue?

Let’s say \($a\) is the total amount of dollar that Sue saved earlier than Alan, \($x\) is the total amount of dollar,including today, Sue and Alan started to save at the same time, and \($y\) is the total amount of dollar that Sue and Alan will save in the future.

We want to know that in how many days from today will Alan have saved one-half as much as Sue.
Therefore, when \($(x+y)\) equals to \($\frac{a+x+y}{2}\), the value of \(y\) will indicate how many days have passed from today that Alan have saved one-half as much as Sue.


(1) As of today, Alan has saved 7 dollars and Sue has saved 27 dollars.

-> At the end of today, Alan has saved \(x=7\), and Sue has saved \(a+x=27\).
-> Substitute to the original equation, \(7+y=\frac{27+y}{2}\)->\(y=13\).
-> Therefore, in 13 days from today, Alan will save one-half as much as Sue.
-> Sufficient

(2) Three days from today, Alan will have saved one-third as much as Sue.

-> \(x+3=\frac{a+x+3}{3}\)
-> we can’t find value of \(x\) and \(a\)
-> Insufficient

Posted from my mobile device

(1) As of today, Alan has saved 7 dollars and Sue has saved 27 dollars.

We're told that each person will continue to save one dollar a day. At some point, Alan will save half of what Sue has. We don't need to calculate this -- simply knowing we can is enough. SUFFICIENT.

(2) Three days from today, Alan will have saved one-third as much as Sue.

We have a ratio -- not enough information. INSUFFICIENT.

Answer is A.
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