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
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Neo2000
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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
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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Cybermusings
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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!
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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Scott@TargetTestPrep
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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.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 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
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Here's the complete question:
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
Let's first determine the least possible integer.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
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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The prompt requires the following: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
(greatest integer)(next largest integer) < 200.
The answer choices imply that the greatest integer must be 13, 14, 15, or 20
15² = 225 and 20² = 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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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
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