Problem Solving

[phoenix9801]

1-

If x and y are both odd, which of the following cannot be odd?

a) xy
b) 3xy
c) (xy)^2
d) x+y
e) x+y-1

2-
Jessica makes 60% of the income earned between her husband and herself. Her husband earns 2.5 times as much as their neighbor earns. Which of the following is most nearly Jessica's income as a percentage of all three incomes?

a) 0.51%
b) 15%
c) 30%
d) 52%
e) 63%

3-
Jake makes 20% commission on domestic sales and 10% commission on international sales. His international sales last month were double his domestic sales. What percentage of Jake's commission last month came from domestic sales?

a) 25%
b) 50%
c) 75%
d) 80%
e) 100%

[neelgandham]

If x and y are both odd, which of the following cannot be odd?

a) xy - Odd * Odd = Odd
b) 3xy - 3*Odd*Odd = Odd*Odd*Odd = Odd
c) (xy)^2 - (Odd*Odd)^2 = (Odd*Odd)*(Odd*Odd) = Odd
d) x+y - Odd + Odd = Even
e) x+y-1 - Odd + Odd - Odd = Odd

Answer D

You can also do it using an example. Let x = 3 and y = 5
then

a) xy = 3*5 = 15 = Odd number
b) 3xy = 3*3*5 = 45 = Odd number
c) (xy)^2 = (3*5)^2 = 225 = Odd number
d) x+y = 3+5 = 8 = Even number
e) x+y-1 = 3+5-1 = 7 = odd number

[Anurag@Gurome]

1- If x and y are both odd, which of the following cannot be odd?

a) xy
b) 3xy
c) (xy)^2
d) x+y
e) x+y-1

x = 1, y = 3

xy = 3 = odd
3xy = 9 = odd
(xy)² = 9 = odd
x + y = 1 + 3 = 4 (we know that odd + odd = even always), so this is the correct answer.

The correct answer is D.

[neelgandham]

Jessica makes 60% of the income earned between her husband and herself. Her husband earns 2.5 times as much as their neighbor earns. Which of the following is most nearly Jessica's income as a percentage of all three incomes?

Ratio of the Incomes of Jessica and his Husband = 6:4 = 15:10
Ratio of the Incomes of Jessica's Husband and Her Neighbor = 2.5:1 = 10:4
Income of Jessica : Income of her husband : Income of her neighbor = 15:10:4
Jessica's income as a percentage of all three incomes = (15/(15+10+4))*100 = (15/29)*100 ~ 52%

a) 0.51%
b) 15%
c) 30%
d) 52%
e) 63%

[eagleeye]

Hi Phoenix:

1- if x and y are odd, x + y = even , hence D.

2- Let Jessica's income be J, her husband's be H, and that of the neighbor be N.
We are given :
1. J = 0.6 (J+H); => J = 0.6J + 0.6H => 0.4J = 0.6H => H=2/3J
2. H = 2.5N => N = H/2.5 => N = 2H/5, using 1. N = 2/5 * (2/3J) = 4/15J

Now J's %age in the total is J*100%/(J+H+N) = 100* J/(J+2/3J+4/15J) = 100 / (1+2/3+4/15) = 100/(29/15) = 100 *(15/29) ~= 52% Hence D

3- Let Jake's international sales last month be I and domestic sales be D, and total commission be T.
We are given:
1. T = 20%D + 10%I = 0.2D + 0.1I
2. I = 2D then using 2 in 1, we get, T = 0.2D + 0.1 (2D)=> T = 0.4D,
then percentage of commission from domestic sales = 100% * 0.2D/T = 100*0.2D/(0.4D) = 50%.
Hence B

[neelgandham]

Jake makes 20% commission on domestic sales and 10% commission on international sales. His international sales last month were double his domestic sales. What percentage of Jake's commission last month came from domestic sales?

a) 25%
b) 50%
c) 75%
d) 80%
e) 100%

Let the domestic sales be x
Then the International sales is 2x
Then the commission on domestic sales = (20/100)* x = 0.2x and
the commission on International sale = (10/100)*2x = 0.2x

Question = (Commission from Domestic sales / Commission from all the sales) * 100 = ?
= (0.2x/(0.2x+0.2x)) * 100 = 50%

IMO B