Problem Solving

Kris-P cereal is 10% sugar by weight, whereas healthier but less delicious
Bran-D cereal is 2% sugar by weight. To make a delicious and
healthy mixture that Is 4% sugar, what should be the ratio of Kris-P
cereal to Bran-D cereal, by weight?
A) 2/5
(B) 1/4
(C) 2/3
(D) 1/2
(E) 1/3

i have issues regarding how to approach such problems fast....i consume lot of time pondering over the way to start for such problems.please assist me regarding it. :

When Leo imported a certain item, he paid a 7 percent
import tax on the portion of the total value of the item
in excess of $1,000. If the amount of the import tax
that Leo paid was $87.50, what was the total value of
the item?
A) $1,600
(B) $1,850
(C) $2,250
(D) $2,400
(E) $2,750

This question has weird statement i calculated thinking that 7% of total value was 87.50$..my ans was 1250 with it,Which was wrong when i saw the solution, i could not grasp the language i guess.do you guess also feel the same about this question. :!:

'manpreet singh wrote:Kris-P cereal is 10% sugar by weight, whereas healthier but less delicious
Bran-D cereal is 2% sugar by weight. To make a delicious and
healthy mixture that Is 4% sugar, what should be the ratio of Kris-P
cereal to Bran-D cereal, by weight?
A) 2/5
(B) 1/4
(C) 2/3
(D) 1/2
(E) 1/3

i have issues regarding how to approach such problems fast....i consume lot of time pondering over the way to start for such problems.please assist me regarding it. :

Step 1: Plot the 3 percentages on a number line, with the two starting percentages (10% and 2%) on the ends and the goal percentage (4%) in the middle.
P(10%)--------------------4%-------D(2%)

Step 2: Calculate the distances between the percentages.
P(10%)-----------6---------4%----2----D(2%)

Step 3: Determine the ratio in the mixture.
The ratio of P to D in the mixture is the RECIPROCAL of the distances in red.
P : D = 2:6 = 1:3.

The correct answer is E.

Here's another:

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ?

(A) 10%
(B) 33.1/3%
(C) 40%
(D) 50%
(E) 66.2/3%

X = 40% ryegrass, Y = 25% ryegrass, the mixture = 30% ryegrass.

X(40%)--------10--------30%-----5-----Y(25%)

X:Y = 5:10 = 1:2.
Since 1+2 = 3, of every 3 liters, 1 liter must be X and 2 liters must be Y, implying that the fraction of X in the mixture = 1/3 = 33 1/3%.

The correct answer is B.

In response to your second question regarding Leo and his taxes: tax is only paid on the amount "in excess of $1,000." The $1,250 you solved for is the amount over $1,000. Add $1,000 and $1,250 and you get C - $2,250.

GMATGuruNY wrote:

'manpreet singh wrote:Kris-P cereal is 10% sugar by weight, whereas healthier but less delicious
Bran-D cereal is 2% sugar by weight. To make a delicious and
healthy mixture that Is 4% sugar, what should be the ratio of Kris-P
cereal to Bran-D cereal, by weight?
A) 2/5
(B) 1/4
(C) 2/3
(D) 1/2
(E) 1/3

i have issues regarding how to approach such problems fast....i consume lot of time pondering over the way to start for such problems.please assist me regarding it. :

Step 1: Plot the 3 percentages on a number line, with the two starting percentages (10% and 2%) on the ends and the goal percentage (4%) in the middle.
P(10%)--------------------4%-------D(2%)

Step 2: Calculate the distances between the percentages.
P(10%)-----------6---------4%----2----D(2%)

Step 3: Determine the ratio in the mixture.
The ratio of P to D in the mixture is the RECIPROCAL of the distances in red.
P : D = 2:6 = 1:3.

The correct answer is E.

Here's another:

Seed mixture X is 40 percent ryegrass and 60 percent bluegrass by weight; seed mixture Y is 25 percent ryegrass and 75 percent fescue. If a mixture of X and Y contains 30 percent ryegrass, what percent of the weight of the mixture is X ?

(A) 10%
(B) 33.1/3%
(C) 40%
(D) 50%
(E) 66.2/3%

X = 40% ryegrass, Y = 25% ryegrass, the mixture = 30% ryegrass.

X(40%)--------10--------30%-----5-----Y(25%)

X:Y = 5:10 = 1:2.
Since 1+2 = 3, of every 3 liters, 1 liter must be X and 2 liters must be Y, implying that the fraction of X in the mixture = 1/3 = 33 1/3%.

The correct answer is B.

THANKS A TON MITCH!!! It is a lightening fast alternative,just 6 secs i guess,still i wonder the concept behind this logic of number line usage for this problem.

internetstanley wrote:In response to your second question regarding Leo and his taxes: tax is only paid on the amount "in excess of $1,000." The $1,250 you solved for is the amount over $1,000. Add $1,000 and $1,250 and you get C - $2,250.

Thanks buddy.
I understood your reasoning,maybe i should be careful with the subtle details of the statements.

Hey check this out. Hope it helps.
Consider x = total weight of Kris- P cereal taken in mix for making 4% cereal mix
and y = total weight of Bran- D cereal taken in mix for making 4% cereal mix

then total weight of 4% mix = x + y

then weight of sugar in this mix = 4% of ( x + y) = 4/100* (x+y)--------A

Now this should be equal to the sum of the weight os sugar in each type of cereal.


1. Now Sugar in Kris-P = 10% of x = 10/100 * x
2. Sugar weight in Bran-D = 2% of y = 2/100 * y
3. Sum of 1. and 2. equals A i.e 4/100* (x+y)


we get 10x + 2y = 4(x+y)

Solve for x/y, and you will get x/y = 1/3.
Please correcct me, if I got it wrong.

very good reasoning,i like it,but you should check out the solution given by mitch as its way too fast method i have know till now....

Very true. Mitch's method is way too good.
I already made a note of it.
Thanx Manpreet. Thanx Mitch.[/img]

Glad you like it,It worth making a note my friend...could save you TONS of time!!