nextTarget wrote:Please help to solve the below DS problem

Bob visited a book fair and bought a certain no. of books. he estimated the total cost on these books by rounding the cost on each of these books to the nearest dollars. was the actual cost minus the estimated cost less than 15 dollars?

1) Bob bought a total of 25 books.
2) the estimated price of 80% of the books is greater than the actual price?

Hi!

Bob certainly wouldn't make it very far in the accounting world (although I think he may have worked for Enron).

Let's start with Step 1 of the Kaplan Method for DS: Analyze the question stem.

We know that Bob rounds off book prices to the nearest dollar and want to know if "the actual cost minus the estimated cost is less than $15". Putting that question in our own words:

Was Bob less than $15 under in his estimation?

(If Bob overestimated, then actual cost - estimated cost would be negative, giving us an automatic "yes" answer.)

How can we tell if he was less than $15 under - by looking at the extreme case of him rounding down on every book by 49 cents. (If a book cost $1.49, he'd round down to $1; if a book cost $1.50, he'd round up to $2.)

To the statements!

(1) Bob bought 25 books.

With 25 books, the max underestimation is 25 * $.49 which is a bit less than $12.50. Is $12.50 less than $15? YES! (1) is sufficient, eliminate B, C and E.

(2) the estimated price of 80% of the books is greater than the actual price.

Sadly, no help here. Picking numbers (a key DS strategy) shows that we can get both a YES and a NO answer.

case 1: Bob buys 1000 books. For 800 of them (80%), Bob overestimates by 1 cent. For 200 of them, Bob underestimates by 49 cents. So, we have:

Overestimation: 800 * 1 cent = $8
Underestimation: 200 * 49 cents = $98
Total underestimation: $90

Is $90 < $15? NO

case 2: Bob buys 1000 books. For 800 of them, Bob overestimates by 50 cents; for 200 of them, Bob underestimates by 1 cent. Even without doing any math, we can see that the net total will be overestimation, giving us an automatic YES answer.

Sometimes yes, sometimes no, insufficient! Eliminate D.

Note: as long as you can visualize both possibilities, there's no need to do any actual calculations. A large part of your DS success will be related to your ability to avoid math!

(1) is sufficient, (2) isn't: choose A!

Thanks Stuart..

But I still have doubt in 1st statement.
Cant Bob overestimate the cost for some of the books? How can we assume that he is just underestimating the cost

nextTarget wrote:Thanks Stuart..

But I still have doubt in 1st statement.
Cant Bob overestimate the cost for some of the books? How can we assume that he is just underestimating the cost

Hi!

We're not assuming anything (never assume in DS!) - we're intentionally looking at the most extreme case to see if it's possible to get a "NO" answer to the question.

If Bob overestimates some books, then he'd be under by even less than our extreme possibility, pushing him even further towards a "YES" answer.

NextTarget,

So the actual cost can be either greater than (for e.g., if each book was for $1.7 than the estemated cost for each book would be $2 and the net estimated cost would be more than actual cost.)the estimated cost or less than it (The nearest integer cost could less than the actual cost for e.g., if all books were 1.3 they would be estimated at 1$ each and the estimated cost would be less than the actual cost. )

Now value (Actual Cost- Estimated Cost) could be thus either positive or negative.
If negative, than the diff. is automatically less than 15$ and we dont need any more information.
but we need to make sure for the case when the value is positive.

Rest is very well explained by stuart.
Hope this helps

Thanks Stuart, Thanks Smith..

Now I got it.. we have already taken the extreme case.

Thanks for your valuable efforts..