Q) Ellen can purchase a certain computer at a local store at the price of p dollars and pay a 6 percent sales tax . Alternatively , Ellen can purchase the same computer from a catalog for a total of q dollars , including all taxes and shipping costs . Will it cost more for Ellen to purchase the computer from the local store than from the catalog ?
(1) q-p < 50
(2) q = 1150

1 is insufficient because it does not tell anything about p and q. lets say P=10, q=60

Then cost at p = 10+ 0.6= 10.6
cost at q = 60 answer is NO.

lets say p= 10,000 and q = 10, 050

cost at p = 10,000+ 600 = 10,600
cost at q = 10,050 answer is Yes ====> stmnt 1 is insufficient.

2. again nothing is said about P. hence stmnt 2 is not sufficicient.


Combining 1 and 2 will answer the question. Hence C.

Question - Price at local store = 1.06p and price at catalog = q.

Seeing this we need some relation between p and q.

Statement (2) insufficient. (doesn't give any info on p).

Statement (1):q-p<50 or p>q-50.
Substituting in 1.06p, the price at local store will be greater than 1.06(q-50).
so 1.06q - 50*1.06. Now here unless we know q we cannot say the total.

Statement 1 and 2 together : 1.06*1150 - 50*1.06 > p, implies that p has to greater than 1150. So sufficient.
Answer C.

can someone help here? i manipulated the equations to look at option C.

q-p < 50
q = 1150

1150 - p < 50
1150 < 50 + p
1100 < p
p > 1100

if we know p is greater than 1100, and q is 1150. p could be equal to 1150 therefore i chose E.

what is wrong with this process? there is no crazy multiplication, seems like a simple inequality.

missrochelle wrote:can someone help here? i manipulated the equations to look at option C.

q-p < 50
q = 1150

1150 - p < 50
1150 < 50 + p
1100 < p
p > 1100

if we know p is greater than 1100, and q is 1150. p could be equal to 1150 therefore i chose E.

what is wrong with this process? there is no crazy multiplication, seems like a simple inequality.

Your algebra is correct, but you're forgetting the 6% tax.

Whenever a problem gives an upper or lower limit, plug in the limit in order to see how the problem is restricted.

Let's plug in p=1100 (the lower limit for p).
If p=1100, cost = 1.06*1100 = 1166.
Since p>1100, cost>1166.

Now we know purchasing through the store will cost more than $1166.

Since q=1150, and 1150<1166, purchasing through the catalog is cheaper.

The correct answer is C.