Ratios and fractions....unclear wording

[Mo2men]

A certain cleaning product is composed of water, soap, and fragrance. If the ratio of water to soap is 2:1 and the ratio of soap to fragrance is three times greater, what is the ratio of water to fragrance after half of the water evaporates?

A. 1:12
B. 1:6
C. 2:1
D. 3:1
E. 6:1

Source: Veritas


I do not understand the sentence "the ratio of soap to fragrance is three times greater". greater of what??

[GMATGuruNY]

A certain cleaning product is composed of water, soap, and fragrance. If the ratio of water to soap is 2:1 and the ratio of soap to fragrance is three times greater, what is the ratio of water to fragrance after half of the water evaporates?

A. 1:12
B. 1:6
C. 2:1
D. 3:1
E. 6:1

The blue portion conveys that the ratio of soap to fragrance is 3 times the ratio of water to soap:
Since W/S = 2/1, we get:
S/F = 3(2/1) = 6/1.

Ratios can be MULTIPLIED.
W/F = W/S * S/F.
In the equation above, the values in red CANCEL OUT.
Subsituting W/S = 2/1 and S/F = 6/1 into W/F = W/S * S/F, we get:
W/F = 2/1 * 6/1 = 12/1.

The resulting ratio indicates that there are 12 liters of water for every 1 liter of fragrance.
After 1/2 the water evaporates, there will be 6 liters of water for every 1 liter of fragrance.

The correct answer is E.

[DavidG@VeritasPrep]

A certain cleaning product is composed of water, soap, and fragrance. If the ratio of water to soap is 2:1 and the ratio of soap to fragrance is three times greater, what is the ratio of water to fragrance after half of the water evaporates?

A. 1:12
B. 1:6
C. 2:1
D. 3:1
E. 6:1

Source: Veritas


I do not understand the sentence "the ratio of soap to fragrance is three times greater". greater of what??

Hm. I think we meant "three times the value of the former ratio," so that if the ratio of water to soap is 2:1, or 2/1, then the ratio of soap to fragrance is 6/1 or 6:1. I'll make an inquiry to the editorial powers-that-be.

(The reason the language is ambiguous is that 300% of x is 3x, but 300% greater than x is x + 3x = 4x. The latter interpretation wouldn't work here.)

Back to the question. Notice that soap is in both ratios, so let's pick a number for the soap. Call it 6 units. This would make water 12 units (there's twice as much water) and fragrance 1 unit. So we have:

soap: 6
water: 12
fragrance: 1

If half the water evaporates, we're down to 6 units of water, giving us a 6:1 ratio of water to fragrance. So the answer is E

[Jay@ManhattanReview]

A certain cleaning product is composed of water, soap, and fragrance. If the ratio of water to soap is 2:1 and the ratio of soap to fragrance is three times greater, what is the ratio of water to fragrance after half of the water evaporates?

A. 1:12
B. 1:6
C. 2:1
D. 3:1
E. 6:1

Source: Veritas


I do not understand the sentence "the ratio of soap to fragrance is three times greater". greater of what??

Hi Mo2men,

It seems that the complete question is not posted. It should probably be: "the ratio of soap to fragrance is three times greater than the ratio of water to soap."

So, we have,

Water : Soap = 2 : 1

and Soap : Fragrance = 3*(2 : 1) = 6 : 1

Since the ratio value for 'Soap' in 'Soap : Fragrance' ratio is '6', and that in 'Water : Soap = 2 : 1' is '1,' we can multiply 'Water : Soap = 2 : 1' ratio by 6 so that the ratio value for Soap matches that from the ratio Soap : Fragrance.

So, Water : Soap = 2 : 1 = (6*2) : (6*1) = 12 : 6

Or, Water : Soap : Fragrance = 12 : 6 : 1

Since half the water evaporated, the ratio value of Water = 12/2 = 6.

Thus, the revised ratio: Water : Soap : Fragrance = 6 : 6 : 1

Or, the ratio of Water : Fragrance =[spoiler] 6 : 1[/spoiler]

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Word Problems Guide

-Jay
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Hi Mo2men,

You can think of the ratios in this question in terms of some real-world example (and TEST VALUES):

"The ratio of water to soap is 2:1".... For every 2 ounces of water, there's 1 ounce of soap.

"the ratio of soap to fragrance is three times greater..."

This part of the prompt is oddly phrased, but the 'intent' of it is to mean for every 6 ounces of soap, there's 1 ounce of fragrance.

Thus, if we have....
1 ounce of fragrance, we have
6 ounces of soap, so we have
12 ounces of water

IF half of the water evaporates, then the ratio of water to fragrance is 12/2 to 1 = 6 to 1

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[Matt@VeritasPrep]

A certain cleaning product is composed of water, soap, and fragrance. If the ratio of water to soap is 2:1 and the ratio of soap to fragrance is three times greater, what is the ratio of water to fragrance after half of the water evaporates?

A. 1:12
B. 1:6
C. 2:1
D. 3:1
E. 6:1

Source: Veritas


I do not understand the sentence "the ratio of soap to fragrance is three times greater". greater of what??

Greater than the only other ratio explicitly stated, the ratio of water to soap. So we've got:

W/S = 2/1

S/F = 3 * (2/1) = 6/1

[Jeff@TargetTestPrep]

A certain cleaning product is composed of water, soap, and fragrance. If the ratio of water to soap is 2:1 and the ratio of soap to fragrance is three times greater, what is the ratio of water to fragrance after half of the water evaporates?

A. 1:12
B. 1:6
C. 2:1
D. 3:1
E. 6:1

We are given that the the ratio of water to soap is 2 : 1, and since the ratio of soap to fragrance is 3 times greater, we have 6 : 1 as the ratio of soap to fragrance.

We can multiply the ratio of water to soap by 6 and we have: water to soap = 12 : 6

So we have:

water : soap : fragrance = 12 : 6 : 1

Since half of the water evaporates, we have:

water : soap : fragrance = 6 : 3 : 1, and thus the ratio of water to fragrance is 6 to 1.

Answer: E