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Ratio and Proportion


GMAT Data Suffficiency RephrasingTo score 700+ on the GMAT, test takers must develop a strategy to answer the Quant questions in 2 minutes and Verbal questions in 1 minute & 20 seconds. Data sufficiency questions can be solved well within the 2-minute mark, most likely in 1 minute and 30 seconds if the conditions and question are rephrased. Not all questions will be required to be rephrased but there are certain conditions where this technique is extremely useful, especially when concepts in Ratio & Proportion, Equations, Inequalities & Divisibility are tested.

Equations

This is the most common question type where rephrasing the conditions might be useful, especially in quadratic equations, and questions that require finding roots.

Let us look into a quadratic equation question type

For the following equations with positive roots, the value of k is greater than one

1) 3x^2 +5x + 2k = 0
2) (x+1)(3x+2) + 2k - 2 = 0

1) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.

2) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.

3) BOTH...

Categories : Ratio and Proportion

Ratio and ProportionJohn and Walter have their incomes in the ratio 7 : 5. The expenses of John, Walter and Nancy are in the ratio 9 : 7 : 4. If Nancy spends $2800 and Walter saves $1100, how much is John’s saving is?

A) $2000
B) $2100
C) $2200
D) $2300

Solution: There is some common element hidden in these type questions pertaining to Ratio and Proportion. If you can find that out, the rest of the solution is a cakewalk.

Let the expenses of John, Walter and Nancy be 9y, 7y and 4y respectively.
Thus, 4y = 2800
=> y = 700

Now, let the incomes of John and Walter be 7x and 5x respectively.

Equation(1)…………Income – Expense = Saving

Plugging in values for Walter,

5x – 7y = 1100
=> 5x – 7*700 = 1100
=> 5x = 1100 + 4900
=> 5x = 6000
=> x = 1200

Plugging in values for John, we get,

7x – 9y = Saving
7*120 – 9*700
=> 8400 – 6300
=> $2100

Thus, John’s saving is $2100

Correct Answer: B

About the Auth...

Categories : Ratio and Proportion

A proportion is represented by two ratios which are equated to each other. In GMAT Quant questions, we would be presented with one variable and three values for proportions. Reduce the ratio in either side to the lowest possible value before cross-multiplying.

For example , a proportion can be presented as a/b = c/d or a:b = c:d

So as per our strategy reduce a/b to the smallest possible fraction

ex: 24/10 should be translated to 12/5

GMAT Proportion: A football field is 9600 square yards.  If 1200 pounds of fertilizer are spread evenly across the entire field, how many pounds of fertilizer were spread over an area of the field totaling 3600 square yards?

A. 450
B. 600
C. 750
D. 2400
E. 3200

The key word here is “spread evenly”. This implies that the relationship of fertilizer per square foot is uniform, and you can set equal the relationship of the wholes to the relationship of the parts.

A/F = 9600/1200 = 3600/x

Clearly, we can eliminate the zeros on the left side:

9600/1200 = 3600/x

96/12 = 3600/x

Then we can divide 96/12:

8 = 3600/x

Here, we can still reduce left-to-right, by canceling 4 in both:

2 = 900/x

Oh wait! There’s more! Both 2 and 900 are divisible by 2!
...

Categories : Ratio and Proportion

Ratio is a math concept that is vital in your post-MBA journey. It allows you to compare variables and provide a means to divide the variable with a common factor. “The ratio of boys to girls is seven to two” can be expressed as the proportion: B/G = 7/2. Do with this what you like: 7G = 2B or B = 7G/2, whatever. Forget the “:” with ratios.

GMAT writers love to provide ratios (which are multiplicative relationships) and then add an absolute component (addition/subtraction). Note that when you have a ratio like B/G = 7/2, we don’t actually know the number of girls and boys. There can be 14 boys and 4 girls, or 70 boys and 20 girls. Questions that insert absolute numbers should be taken with caution. For example:

At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 13. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 3 to 16. How many cooks does the restaurant have?

A. 4
B. 6
C. 9
D. 12
E. 15

The key here is setting up the equation. Since we don’t know the initial scale of the number of cooks and waiters, we can express this scale by “x”.
C/W = 3x/13x.

Notice that whatever x is, the ratio will hold true. (x must be...




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