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Word problem questions (deck of cards etc)

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Word problem questions (deck of cards etc)

by oex85 » Sat Jul 09, 2011 9:09 am
Did the first of the GMAT prep tests today and had some problems from the start with two word problems.

1. For a finite sequence of nonzero numbers, the number of variatinos in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative. What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6?

Alternatives: One, two, three, four or five.

Just can't wrap my head around this text. Don't want to give my faulty answer just yet...


2. 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 product is between 15 and 200, then the least and greatest integers on the cards could be:

- 3 and 15
- 3 and 20
- 4 and 13
- 4 and 14
- 5 and 14


Looks like I'm gonna have to work on my word problems. Appreciate any help with these Q:s!
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by sgarnepudi » Sat Jul 09, 2011 9:39 am
Q1: Ans is 3.

Q2: Ans is 4 and 13.

Frankenstein is correct.
Last edited by sgarnepudi on Sat Jul 09, 2011 9:51 am, edited 1 time in total.
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by Frankenstein » Sat Jul 09, 2011 9:44 am
Hi,
Q1 is nothing but asking for sign changes. A sign change is + to -, and - to +
Consider 1,-3,2,5,-4,-6. sign changes from 1 to -3, -3 to 2 and 5 to -4
So, answer is three

Q2)Product of a number and next larger number means if you pick a number n, the product is n*(n+1)
Go from options,
if we pick 3, n(n+1) is 12 not in the range (15,200)
So, A,B are out
if n = 4, n(n+1) = 20 ..fine in the range (15,200)
if n = 13, n(n+1) = 182 ..fine in the range (15,200)
if n= 14, n(n+1) = 14*15 = 210 outside the range (15,200)

Hence, C
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by oex85 » Sat Jul 09, 2011 5:26 pm
Frankenstein wrote:Hi,
Q1 is nothing but asking for sign changes. A sign change is + to -, and - to +
Consider 1,-3,2,5,-4,-6. sign changes from 1 to -3, -3 to 2 and 5 to -4
So, answer is three

Q2)Product of a number and next larger number means if you pick a number n, the product is n*(n+1)
Go from options,
if we pick 3, n(n+1) is 12 not in the range (15,200)
So, A,B are out
if n = 4, n(n+1) = 20 ..fine in the range (15,200)
if n = 13, n(n+1) = 182 ..fine in the range (15,200)
if n= 14, n(n+1) = 14*15 = 210 outside the range (15,200)

Hence, C
Thank you! Great answer. I really need to get better translating text into equations... However, this piece of text just confuses me so much:

"the number of variatinos in sign is defined as the number of pairs of consecutive terms of the sequence for which the product of the two consecutive terms is negative"

Guess I should ignore this part and just read:

"What is the number of variations in sign for the sequence 1, -3, 2, 5, -4, -6? "

Need some practice with the word problems.

Thanks again.
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by amit2k9 » Mon Jul 18, 2011 10:51 pm
a (1,-3); (-3,2) ; (5,-4) hence 3.

b 15 < n(n+1) < 200
means,

n * (n+1) = 4*5 = 20
and 13*14 = 182.

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