To 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.
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 statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
4) EACH statement ALONE is sufficient to answer the question asked.
5) Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
If test takers straight away solve each equation separately without finding any relation between the two, the target of correctly answering the question in 1 minute and 30 seconds will not be reached. When it is a quadratic equation, just look at how the equation is formulated and notice if there are any relationship between the two equations.
As you might have noticed, on solving equation 2
(x+1)(3x+2) + 2k - 2 = 0
3x^2 +5x + 2k
Both Statements are equal
Can we conclusively say that the value of k is greater than 1? The question tells us that it has positive roots.
To get positive roots for 3x^2 +5x + 2k
X has to be 3 and 2 or k = 1
Therefore, K is equal to 1.
Correct Answer: D, Both statements independently will give us the answer.
Another scenario where the two statements might be the same on rephrasing is inequality questions. The options can be tricky when absolute value concepts are tested
What is the value of x?
1) |x-3| < -2
2) |x^2 + 5x + 6| > 0
Rephrasing statement 1, we get
|x-3| < -2
(x-3) < -2
X < 1
-(x-3) < -2
-x +3 < -2
X > 5
X < 1 and x > 5 -> Rephrasing Statement 1
Rephrasing statement 2, we get
|(x+3) (x+2)| > 0 or
= (x+3)(x+2)> 0 and - (x+3)(x+2) > 0
= (x+3)(x+2)> 0 and (x+3)(x+2) < 0 (Sign reversed on multiplying negative on both sides
of the equation -> Rephrasing Statement 2
Rephrasing the conditions in the equation, we get:
What is the value of x?
1) X < 1 and x > 5
2) (x+3)(x+2)> 0 and (x+3)(x+2) < 0
This might look like a lot of calculation but the rules of absolute value inequalities are simple
Divisibility – Rephrasing Question
Not all GMAT Data Sufficiency rephrasing is operated on the two conditions. Carefully rephrasing questions can lead to easier problem solving.
Is 3+ 2n divisible by 3?
1) n is odd
2) n^2 is a multiple of 3
If you rephrase the question, it would look like
Is 2n a multiple of 3?
Ratio & Proportion - Rephrasing Question & Conditions
Another common GMAT DS question where rephrasing is effective is the Ratio and Proportion question.
Q) At the start of the annual shareholders conference, the number of men and women were in the ratio 4:5. 100 participants joined the conference 10 minute late, what is the new ratio of men and women?
1) If two more men were to join the conference after 20 minute, the ratio of men and women will be 7:8
2) 50 participants left the conference after 30 minutes, changing the ratio of men and women to 3:4.
Rephrasing questions and conditions to equations are most effective for solving lengthy GMAT data sufficiency questions.
Q) N participants joined a conference with x men and y women in a conference such that x:y = 4:5. 100 participants joined the conference 10 minute late, what is x:y?
1) (X+2)/ y = 7/8
2) N – 50, x/y = 3/4
Once you have rephrased the question to equations, it becomes easier to solve this GMAT DS Question.
With Statement 1, we get two equations in x and y, which is sufficient to find x:y
With Statement 2, we get equations with x, y and N, which is not sufficient to find the ratio, x: y
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