deck of cards

[shibal]

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 by the next larger integer. if each possible prodcut is between 15 and 200, then the least and gratest integers on the cards could be

oa 4and 13

[VP_Jim]

This question is really just a confusing way of asking you:

When multipied together, what two consecutive integers are just above 15? And, when multiplied together what two consecutive integers are just below 200?

Try out some numbers --

3x4 = 12. That's less than 15, so we've violated the terms of the question (in that we'd have 12, 13, and 14 as possible values - the problem says that 15 is the lowest possible value). So, we need to go up 4x5=20. That's within our range, so 4 is the lowest possible value.

Now let's test out the high end.

14x15=210. That's too big, since 200 is the highest possible value in the game. We need to drop down to 13x14=182. 182 is within our range (under 200), so 13 is the highest possible value.

So, the answer is 4 and 13.

Note that the problem says that the products are "BETWEEN 15 and 200." That does NOT mean that 15 and 200 must be included - those are just the boundaries. So, in this game, the ACTUAL extreme values are 4x5=20 and 13x14=182, which are BETWEEN 15 and 200.

Tricky!

[shibal]

tricky but really easy tough.... the active reading for the verbal part should have been used now....

[VP_Jim]

So true, so true... lots of (most?) GMAT quant problems seem "easy" once you see the trick!

[real2008]

This question is really just a confusing way of asking you:

When multipied together, what two consecutive integers are just above 15? And, when multiplied together what two consecutive integers are just below 200?

Try out some numbers --

3x4 = 12. That's less than 15, so we've violated the terms of the question (in that we'd have 12, 13, and 14 as possible values - the problem says that 15 is the lowest possible value). So, we need to go up 4x5=20. That's within our range, so 4 is the lowest possible value.

Now let's test out the high end.

14x15=210. That's too big, since 200 is the highest possible value in the game. We need to drop down to 13x14=182. 182 is within our range (under 200), so 14 (13) is the highest possible value.

So, the answer is 4 and 14 (13).

Note that the problem says that the products are "BETWEEN 15 and 200." That does NOT mean that 15 and 200 must be included - those are just the boundaries. So, in this game, the ACTUAL extreme values are 4x5=20 and 13x14=182, which are BETWEEN 15 and 200.

Tricky!

please check....

[VP_Jim]

You're right- 4 and 13. Typo.

[xilef]

wait, where is the typo, the answer is '4 and 13' as Jim had in his original post.

[VP_Jim]

I edited the original to get rid of the typo, in hopes of easing confusion. Looks like it backfired!

[pallasy]

This question is really just a confusing way of asking you:

When multipied together, what two consecutive integers are just above 15? And, when multiplied together what two consecutive integers are just below 200?

Try out some numbers --

3x4 = 12. That's less than 15, so we've violated the terms of the question (in that we'd have 12, 13, and 14 as possible values - the problem says that 15 is the lowest possible value). So, we need to go up 4x5=20. That's within our range, so 4 is the lowest possible value.

Now let's test out the high end.

14x15=210. That's too big, since 200 is the highest possible value in the game. We need to drop down to 13x14=182. 182 is within our range (under 200), so 13 is the highest possible value.

So, the answer is 4 and 13.

Note that the problem says that the products are "BETWEEN 15 and 200." That does NOT mean that 15 and 200 must be included - those are just the boundaries. So, in this game, the ACTUAL extreme values are 4x5=20 and 13x14=182, which are BETWEEN 15 and 200.

Tricky!

Jim, why did you automatically assume 14 must be multiplied by 15? I understand the instructions say to multiply by the next highest integer, but since it's a "deck of cards," wouldn't 14 be the highest integer (J=11, Q=12, K=13, A=14)? If so, wouldn't 14 just need to be multiplied by 14 since there is no larger integer? 14x14 = 196, which means the answer would be 4 & 14?