Data Sufficiency

Fabio designer fashion store has become so popular that he can raise the prices every day. Each day, he raises the price of his designer pants by one dollar more than he raised it the previous day. Given that the price on Sunday the 15th was $700, what was the price on Saturday the 21st?

(1) The price on Thursday was $746.
(2) The difference between the price on Monday the 16th and Sunday the 22nd was $81.


OA:D

I think it should be B

Statement 1 - Thursday does not have a date. (not sure if we can assume it the first thursday)

Statement 2:

Price difference for 6 days given as 81.

Thats is (11+12+13+14+15+16 = 81).

We know cost on Sunday (15th) - X = 700

Therefore, cost on 21st would be X+ 11+12+13+14+15 = 765. Sufficient.

If date was mentioned in A, I would mark D

dell2 wrote:Fabio designer fashion store has become so popular that he can raise the prices every day. Each day, he raises the price of his designer pants by one dollar more than he raised it the previous day. Given that the price on Sunday the 15th was $700, what was the price on Saturday the 21st?

(1) The price on Thursday was $746.
(2) The difference between the price on Monday the 16th and Sunday the 22nd was $81.


OA:D

Let the increment on 1st day be x
Let p(i) be the price on ith day. p(1) = 700 (the 1st day)

p(2) - P(1) = x
p(3) - p(2) = x + x + 1 = 2x + 1
p(4) - p(3) = x + x + 1 + x + 2 = 3x + ( 1 + 2 )

The last part ( ( 1 + 2) in the last equation ) is an AP with 1 as the 1st term of the AP and (n - 2) as the last term. Let this sum be represented by AP(n)
So we can write

p(n) - p(n-1) = (n - 1)x + AP(n)

Now, according to (1), we have the price on Thursday.
We already know the price on Saturday.
The no. of days between the 2 dates is known. p(n) and p(1) are known. So we see that we can find the value of x. If we get the value of x then we can find the value on any other day. So sufficient

(2) gives the difference between the prices on 2 days. Which will again be sufficient to get the value of x and hence is sufficient

So D

we need to find the amount of increase and then apply consecutive order (hint -> increase by one)

st(1) suggests the amount of increase x, 746-(4x+6)=700 OR 40=4x and x=10
price on Saturday -> 700+(6*10+15)=775

x,x+1, x+2, x+3, x+4, x+5 <- all six days OR 6x+[(1+5)/2]*5 <- sum from average of consecutive order

st(2) price on Monday is the price after initial increase x, and the price on Sunday is the price of 7x+21. The difference Sunday-Monday is equal to 7x+21-x=6x+21 which is set equal to 81 as well. Hence 6x+21=81, x=10 and the price on Saturday is 700+(6x+15)=775

d

dell2 wrote:Fabio designer fashion store has become so popular that he can raise the prices every day. Each day, he raises the price of his designer pants by one dollar more than he raised it the previous day. Given that the price on Sunday the 15th was $700, what was the price on Saturday the 21st?

(1) The price on Thursday was $746.
(2) The difference between the price on Monday the 16th and Sunday the 22nd was $81.


OA:D

dell2 wrote:Fabio designer fashion store has become so popular that he can raise the prices every day. Each day, he raises the price of his designer pants by one dollar more than he raised it the previous day. Given that the price on Sunday the 15th was $700, what was the price on Saturday the 21st?

(1) The price on Thursday was $746.
(2) The difference between the price on Monday the 16th and Sunday the 22nd was $81.


OA:D

Since the price is raised by $1 more each day, the price increases comprise a set of consecutive integers.
Given a set of consecutive integers:
Median = average = sum/number.
Sum = number * average.

The solution below presumes that statement 1 refers to Thursday the 19th.

Statement 1: The price on Thursday was $746.
Since Thursday = 746 and Sunday = 700, the sum of the increases between Sunday and Thursday = 46.
Median increase for the first 4 days = sum/number = 46/4 = 11.5.
Thus, the increase on Tuesday = $11 and the increase on Wednesday = $12.
Thus, the increases Monday through Saturday comprise the consecutive integers 10 through 15.
Sum of the increases = number * average = 6 * 12.5 = 75.
Thus, the price on Saturday = 700+75 = 775.
SUFFICIENT.

Statement 2: The difference between the price on Monday the 16th and Sunday the 22nd was 81.
Thus, the sum of the increases for the 6 days Tuesday through Sunday = 81.
Median = sum/number = 81/6 = 13.5.
Thus, the increase on Thursday = $13 and the increase on Friday = $14.
The result is the same set of consecutive integers determined in Statement 1, implying that the price on Saturday will be $775.
SUFFICIENT.

The correct answer is D.

Hi Mitch,
I'm not very clear with this.

The solution below presumes that statement 1 refers to Thursday the 19th.

How did you assume this? Aren't we NOT supposed to assume anything in DS questions?

Statement 1: The price on Thursday was $746.
Since Thursday = 746 and Sunday = 700, the sum of the increases between Sunday and Thursday = 46.
Median increase for the first 4 days = sum/number = 46/4 = 11.5.
Thus, the increase on Tuesday = $11 and the increase on Wednesday = $12.
Thus, the increases Monday through Saturday comprise the consecutive integers 10 through 15.

Sum of the increases = number * average = 6 * 12.5 = 75.

I didn't understand this. How ru getting 12.5 here?

Is there any other way to solve this problem? Pl explain.

urshohini wrote:Hi Mitch,
I'm not very clear with this.

The solution below presumes that statement 1 refers to Thursday the 19th.

How did you assume this? Aren't we NOT supposed to assume anything in DS questions?

Since the price on Sunday the 15th = 700, and the price INCREASES every day, a price of $746 implies a date AFTER the 15th. Since no date is specified, Statement 1 must be referring to the first Thursday after Sunday the 15th. If statement 1 were referring to a later Thursday, a specific date would have been specified.

Sum of the increases = number * average = 6 * 12.5 = 75.

I didn't understand this. How ru getting 12.5 here?

Is there any other way to solve this problem? Pl explain.

Here again is the beginning of my explanation for Statement 1:

Statement 1: The price on Thursday was $746.
Since Thursday = 746 and Sunday = 700, the sum of the increases between Sunday and Thursday = 46.
Median increase for the first 4 days = sum/number = 46/4 = 11.5.
Thus, the increase on Tuesday = $11 and the increase on Wednesday = $12.
Thus, the increases Monday through Saturday comprise the consecutive integers 10 through 15.

The increases Monday through Saturday = 10,11,12,13,14,15.
Given evenly spaced integers:
Average = median = (biggest+smallest)/2 = (10+15)/2 = 12.5.
Sum = number of integers * average = 6 * 12.5 = 75.
Thus, the price on Saturday = 700+75 = 775.

Truth be told, no math is needed for this problem.

Having recognized that the increases will comprise a set of CONSECUTIVE INTEGERS, we should realize when we evaluate statement 1 that only ONE PARTICULAR SET of 4 consecutive integers will yield a sum of 46.
Thus, statement 1 offers sufficient information to determine by how much the price will increase every day, enabling us to determine the price on Saturday the 21st.

The same reasoning can be applied to statement 2: only ONE PARTICULAR SET of 6 consecutive integers will yield a sum of 81.
Thus, like statement 1, statement 2 offers sufficient information to determine by how much the price will increase every day, enabling us to determine the price on Saturday the 21st.

Yes, I got it now.
Thank you very much for the detailed explanation, Mitch.