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product of integers + word probs

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product of integers + word probs

by LevelOne » Sat Jun 20, 2009 8:09 am
Hello,

Can you give me a quick hand with DS questions below, please?

1) A certain list consists of several different integers. Is the product of all the integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.
(2) There is an even number of integers in the list.

The OA is C but I don't see how it works...as I think it should be E.

The integers could be in the combinations e.g.:
2,-3,-4,5 (product positive)
2,3,-4,5(product negative)
-2,3,4,-5(product positive)

please let me know your ideas.

2) The cost of each adult's ticket for a certain concert was $30, and the cost of each child's ticket for the concert was $24. If Hannah purchased tickets for this concert, what was the average (arithmetic mean) cost per ticket?

(1) Hannah purchased twice as many children's tickets as adult's tickets.
(2) Hannah purchased 4 children's tickets.

I have a bit of a problem with (1), I am getting:
A = adult's tickets
C = children's tickets
x = number of tickets purchased
so we have A = x; C = 2x but we don't have a sum or a number of tickets to conclude that (1) is suff??

3) Robin split a total of $24,000 between two investments, X and Y. If investment Y earns 7% simple annual interest, how much of the total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of the interest annually.
(2) Investment X earns 5% simple annual interest.

I'm a bit struggling to set up an equation for this one. Any suggestions?

Thanks! All OAs will be posted.
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by abhinav85 » Sat Jun 20, 2009 8:22 am
Ques 1 IMO C

Ques 2 IMO A

Ques 3 IMO D
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by LevelOne » Sat Jun 20, 2009 8:53 am
Ques 3 is not D. Can you give a bit more detail behind ques 1-2, pls?
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Re: product of integers + word probs

by rahulg83 » Sat Jun 20, 2009 11:10 am



1) A certain list consists of several different integers. Is the product of all the integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.
(2) There is an even number of integers in the list.

The OA is C but I don't see how it works...as I think it should be E.

The integers could be in the combinations e.g.:
2,-3,-4,5 (product positive) - here product is negative -4*5 = -20
2,3,-4,5(product negative) - OK, u r right
-2,3,4,-5(product positive) - here product is negative, -5*4 = -20

please let me know your ideas.
OA is C, if smallest number is negative, largest no should also be negative, so as to make product positive, we should be worried only when all the integers are negative, so if the number of 'negative' integers is even (from statement 1), yes, the product is positive. Don't worry about numbers greater than 0, their product will always be positive. Also 0 can't be part of any set (IF statement 1 is true), otherwise product of least number and greatest no would be negative (Consider -2,-1,0,1,2 for example)
2) The cost of each adult's ticket for a certain concert was $30, and the cost of each child's ticket for the concert was $24. If Hannah purchased tickets for this concert, what was the average (arithmetic mean) cost per ticket?

(1) Hannah purchased twice as many children's tickets as adult's tickets.
(2) Hannah purchased 4 children's tickets.

I have a bit of a problem with (1), I am getting:
A = adult's tickets
C = children's tickets
x = number of tickets purchased
so we have A = x; C = 2x but we don't have a sum or a number of tickets to conclude that (1) is suff??
Statement 1:
No of Adult tickets = A
No of children's tickets = 2A

Total cost of tickets = A*30 + 2A*24
Mean = Total/3A = (A*30 + 2A*24)/3A, cancel A from numerator and denominator.

Statement 2:
No info on number of Adult's tickets. Insufficient.
3) Robin split a total of $24,000 between two investments, X and Y. If investment Y earns 7% simple annual interest, how much of the total did Robin put into investment Y?

(1) Each investment earns the same dollar amount of the interest annually.
(2) Investment X earns 5% simple annual interest.

I'm a bit struggling to set up an equation for this one. Any suggestions?

Thanks! All OAs will be posted
x+y=24000 --- eqn 1
now interest on y at end of the year = 0.07*y
Statement 1: let r be the rate of interest for investment x

So, at the end of the year, x will earn (r/100)*x

Now 0.07*y=(r/100)*x ---eqn 2

we have 2 equations and 3 variables, Insufficient

Statement 2: r=5 --- eqn 3, no other info, Insufficient

Both statements hence are insufficient, 3 equations, 3 variables

Answer C
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by LevelOne » Sat Jun 20, 2009 12:46 pm
rahulg83, this works. thanks!
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by Patrick_GMATFix » Tue Jun 08, 2010 5:42 am
LevelOne wrote:A certain list consists of several different integers. Is the product of all the integers in the list positive?

(1) The product of the greatest and smallest of the integers in the list is positive.
(2) There is an even number of integers in the list.
[The reply below is copied from this thread]

To have a positive product, we must have an even number of negatives (0, 2, 4...) so that the negatives will cancel out in the multiplication.

REPHRASE: Are there an even number of negatives?

1) Max * Min is positive means Max and Min have the same sign. If they're both positive, then everything is positive and so is the product of all integers. However, if Max and Min are both negative, the product could be negative if we do NOT have an even number of negatives. Example {-3, -2, -1}. NOT SUFFICIENT.

2) By itself, this doesn't tell us whether there is an even number of negatives. Doesn't answer our rephrase.

Merge statements: (2) tells us that we have an even number of values. Since all the values have the same sign (1 says Max and Min have the same sign), either we have all positives or we have an even number of negatives. Either way, the product of all terms will be positive.

The answer is C

If the explanations above don't make sense to you, watch the step-by-step video solution. This is GMATPrep question 1106.

You can practice similar questions by using the Drill Engine to generate timed drills and setting topic='Number Properties' and difficulty='500-600 & 600-700'

Best of luck,
-Patrick
  • Ask me about tutoring.
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