GMAT Prep Problem 3

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RachelAL: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Wed Mar 07, 2007 5:57 am

by RachelAL » Tue Mar 27, 2007 6:14 am

Some of these problems are driving me nuts. I am missing something for sure. Any help would be much appreciated. Thanks!

There is a deck of cards, each card with a positive integer on it. In a multiplication game, a child draws a card and a multiplies by the next largest integer. If each posible product is between 15 and 200, then the least and greatest integers could be:

Answer: 4 and 13

-Rachel

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Source: Beat The GMAT — Problem Solving | Tue Mar 27, 2007 6:14 am

Neo2000: Legendary Member; Posts: 519; Joined: Sat Jan 27, 2007 7:56 am; Location: India; Thanked: 31 times

by Neo2000 » Tue Mar 27, 2007 7:45 am

You know that 15^2 = 225
Which means your number has to be less than 15
14times 15 = 220
So not 14
13times 14 = 192 so definitely 13 was your max value

Similarly 15 = 5x3
It couldnt be 3 since 3times 4 = 12 which is less than 15
4times 5 = 20 so your min value was 4

4,13 was your answer

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RachelAL: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Wed Mar 07, 2007 5:57 am

by RachelAL » Tue Mar 27, 2007 8:04 am

Thanks so much!

-Rachel

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Cybermusings: Legendary Member; Posts: 559; Joined: Tue Mar 27, 2007 1:29 amFollowed by: 2 members; Thanked: 5 times

by Cybermusings » Tue Mar 27, 2007 10:40 am

There is a deck of cards, each card with a positive integer on it. In a multiplication game, a child draws a card and a multiplies by the next largest integer. If each posible product is between 15 and 200, then the least and greatest integers could be:

Answer: 4 and 13

The cards in a deck of cards is 1-13

Therefore the greatest card could be of value 13. Cross verify by using the product value. value of the product = 13*14 = 182 which is less than 200 and hence valid

The smallest card is 1. 1*2 = 2 ; less than 15 hence not possible

Next is 2. 2*3 = 6. Not valid again

Next is 3. 3*4 = 12. Not valid again

Next is 4. 4*5 = 20. hence possible

Cheers!

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by Scott@TargetTestPrep » Sun Aug 26, 2018 6:44 pm

RachelAL wrote:Some of these problems are driving me nuts. I am missing something for sure. Any help would be much appreciated. Thanks!

There is a deck of cards, each card with a positive integer on it. In a multiplication game, a child draws a card and a multiplies by the next largest integer. If each posible product is between 15 and 200, then the least and greatest integers could be:

Since 3 x 4 = 12 and 4 x 5 = 20, we see that 20 is the smallest product between 15 and 200; thus, the least integer must be 4.

Since 13 x 14 = 182 and 14 x 15 = 210, we see that 182 is the largest product between 15 and 200; thus, the greatest integer must be 13.

Answer: 4 and 13

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

GMAT Prep Problem 3

by Brent@GMATPrepNow » Mon Aug 27, 2018 9:22 am

Here's the complete question:

In a certain deck of card has a positive integer written on it. In a multiplication game, a child draws a card and multiples the integer on the card by the next larger integer. If each possible product is between 15 and 200, then the least and greatest integers on the card could be?

A) 3 and 15
B) 3 and 20
C) 4 and 13
D) 4 and 14
E) 5 and 14

Let's first determine the least possible integer.

We'll use the answer choices to help us along...
A) Could the smallest value on the card be 3?
Well, the next larger integer is 4, and 3 x 4 = 12, which is OUTSIDE the given range of 15 to 200
So, we can ELIMINATE A and B

C) Could the smallest value on the card be 4?
The next larger integer is 5, and 4 x 5 = 20, which is WITHIN the given range
So, 4 must be the LEAST possible value on the card
ELIMINATE E

Now, let's determine the greatest possible integer.
The 2 remaining answer choices tell us that the greatest possible integer is EITHER 13 OR 14

Let's test 14 first (WHY? Since we're looking for the GREATEST value, it makes sense to check the biggest value first)
The next larger integer is 15, and 14 x 15 = 210, which is OUTSIDE the given range of 15 to 200
So, we can ELIMINATE D

IMPORTANT: We're not going to waste valuable time testing to see whether 13 works, since we've already eliminated A, B, D and E

Answer: C

Cheers,
Brent

Last edited by Brent@GMATPrepNow on Tue Aug 28, 2018 6:07 am, edited 1 time in total.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Aug 27, 2018 12:57 pm

In a certain deck of cards, each card has a positive integer written on it. In a multiplication game, a child draws a card and multiplies the integer on the card with the next largest integer. If the each possible product is between 15 and 200, then the least and greatest integers on the card would be

A. 3 and 15
B. 3 and 20
C. 4 and 13
D. 4 and 14
E. 5 and 14

The prompt requires the following:
(greatest integer)(next largest integer) < 200.
The answer choices imply that the greatest integer must be 13, 14, 15, or 20
15Â² = 225 and 20Â² = 400.
Implication:
(15)(next largest integer) and (20)(next largest integer) will each yield a product greater than 200.
Eliminate A and D.

Test whether the greatest integer could be 14:
(14)(next largest integer) = 14*15 = 220.
Since the product is above 200 and thus too high, the greatest integer cannot be 14.
Eliminate D and E.

The correct answer is C.

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