In a certain deck of cards, each card has a positive integer written o

Hi All,

Since the answers to this question are numbers, I'm going to TEST THE ANSWERS.

We're told that, after drawing a card, you must multiply the number on the card by the next larger integer and end up with a number between 15 and 200. We're asked for the smallest and largest possible numbers on the cards.

IF the number was 3, then…
3(4) = 12, which is NOT between 15 and 200. Eliminate A and B.

IF the number was 4, then…
4(5) = 20, which IS between 15 and 200. Eliminate E.

Now, on to the biggest number:

IF the number was 13, then…
13(14) = 182
IF the number was 14, then…
14(15) = 210

So, 14 is TOO BIG.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

The part that was confusing to me was the wording, "If each possible product is between 15 and 200..." I took that to mean it had to be 15 at the lowest and 200 at the highest. Since there aren't any perimeters that fit those integers, it burnt up my time and left me frustrated. Learned and moved forward though.

Agreed. I couldn't think of anything other the next consecutive integer and hence used that. Wasn't completely sure but the answer options made sense with this assumption.


Between could mean either - including the extremes or excluding the extremes. It is usually specified when you do need to know it. 15 cannot be represented as a product of two consecutive integers and hence you know that the extremes are not included. Hence giving this information here was no essential.

Another Method:
Look for the square root - 15 square root will be 3.something but 3*4 = 12 (which does not lie in 15 to 200). So 4 must be the smallest integer.
200 square root will be 14.something because 14^2 = 196. 14*15 will be more than 200 so the largest number must be 13.

Answer (C)

Hi,

Im not sure what am I missing in the following logic.

As the question tells that the possible product is going to be between 15 and 200. The lowest pair will be 4 and 5 (4*5=20) and the largest pair is going to be 13 & 14 (13*14=182). Since the question asks " LEAST and GREATEST integers on the cards could be .." - I chose option D since - the least number will be 4 and the greatest 14. What am I missing?

Thanks!

14 cannot be written on the card because in this case 14*(14+1) = 210 > 200.

Since the product is above 15, and since 3 x 4 = 12, we can eliminate answers A and B.

We also see that 4 must be the minimum integer on any of the cards since 4 x 5 = 20, which is the smallest product above 15. We can, therefore, eliminate answer choice E, and we are left to choose between answers C and D.

Let’s check the maximum value from answer choice C.

13 x 14 = 182

13 could be the maximum value. Let’s test answer choice D.

14 x 15 = 210

Since 210 is greater than 200, D is not correct.

Answer: C

My first step was to divide 200/15 which gave me the greatest integer (13) and because there is only one option offering 13 I just went with option C... any comments??

The logic is not sound. The question tells us that the product of the smallest integer with the next integer. Since 3*4 = 12 and 4*5 = 20, the smallest integer must be 4.
200 is the product of the largest integer with the next integer.
Taking a hint from the options, since 13*14 = 182 and 14*15 = 210, the largest number must be 13.
There is no logic to using 200/15

If instead of 200 we had 300,
300/15 would be 20
But the largest integer would be 16 (since 16*17 = 272)

Hi All,
Maybe i got a bit lucky here, but when i solved it. I assume that no card has a value of >13
and only option available was 4 and 13 which is the correct answer.
Am i completely wrong in my assumption ?

Hi hsn81960,

Can you go into a bit more detail about WHY you 'assumed' that no card had a value greater than 13 on it? Did you do any math to clarify your logic or were you just thinking about a 'standard' deck of playing cards (that include 13 cards of each suit)?

GMAT assassins aren't born, they're made,
Rich

Hi Rich,
While i was trying to do the maths in my head. All of a sudden i realized that there arent more than 13 cards in each suit.
So i just thought its an easy question and i need to think through. So immediately picked an option that doesnt have a value more than 13.
Luckily it was the correct choice.

Hi hsn81960,

The prompt tells us NOTHING about the number of cards in the deck nor anything about "suits", so you ultimately did get 'lucky' on this question. As an aside, doing work "in your head" is the WORST way to approach a GMAT question (since you'll be far more likely to make a silly mistake - and those types of mistakes tend to cost Test Takers a LOT of points on Test Day).

GMAT assassins aren't born, they're made,
Rich

I read the question as saying that the card drawn would be multiplied by the next large integer card. As I am looking through the answer choices I know this is not the proper reading of the question because if it was, the smallest card could be 1 (multiplied by the next largest card 15 in order to get a product in the 15-200 range). None of the answer choices have a number below 3, so I know the I must be reading the question incorrectly. I think this question serves as an example of how answer choices can help one figure out what the question is actually asking.

Hi barsellac,

You've discovered something really important about the GMAT - the 5 answer choices can often be quite useful in helping you to determine how to approach a prompt (and even whether you are interpreting the prompt correctly or not). In the Verbal section, the 5 answer choices to SCs can often help to define the specific grammar rules involved and how you can sometimes eliminate answers even after reading just part of the sentence. Continue to take advantage of all of these patterns and you'll find that hitting your Score Goal becomes far easier.

GMAT assassins aren't born, they're made,
Rich

Let's start by determining the value of the SMALLEST possible number on the cards.

The answer choices tell us that the smallest number is 3, 4, or 5.

Given: In a multiplication game, a child draws a card and multiplies the integer on the card by the next larger integer.
If the smallest number is 3, then the next larger integer is 4.
The product 3 x 4 = 12, however the question tells us that all possible products are between 15 and 200
So, the smallest number cannot be 3.

Let's see if 4 can be the smallest possible number
If the smallest number is 4, then the next larger integer is 5, and the product 4 x 5 = 20, which IS between 15 and 200
Since the smallest possible number is 4, the correct answer is either C or D.

Let's test answer choice D, which tells us the LARGEST possible number is 14.
If the largest number is 14, then the next larger integer is 15, and the product 14 x 15 = 210, which is NOT between 15 and 200
So, we can eliminate answer choice D, which means the correct answer must be C

Cheers,
Brent

Hello,

I think you assumed an option here =
"IF the number was 4, then…
4(5) = 20, which IS between 15 and 200. Eliminate E."

IF the number is 5, for option E, it satisfies the criteria 5(6) = 30, which is between 15 and 200,
so at this point in your calculation step, you cant eliminate option E yet.
I understand that it does not affect the answer choice but I thought to bring it up just for reference.

Thanks for the explanation.

Hi princejero,

Since the prompt asks us to find the LEAST and GREATEST integers on the cards, once we determined that 3 was 'too small', but 4 was 'in the range of what we were looking for', we KNOW (based on how the answers are written) what the LEAST integer is (it's 4). That's why we can eliminate Answer E (it states that the LEAST integer is 5 - which is not correct).

GMAT assassins aren't born, they're made,
Rich