sud21 wrote:a is equal to one of the numbers 5/11 , 7/12 , 9/13 , what is the value of a?
1. 5/11 < a < 3/4
2. 11/13 > a > 1/2

Hint:
1. check to see if choices can be broken down into simpler terms or can we compare the choices to a reference point. For example we can see which fractions are greater than 1/2
5/11 is less than 1/2 but 7/12 and 9/13 are greater than 1/2

2. to check if one fraction is greater than another we cross multiply and bigger numerator leads to bigger fraction
for example is 7/12 < 9/13?
is 7/12 < 9/13 = 7*13 < 12*9 = 91 < 108
answer is yes; 7/12 < 9/13

Brent@GMATPrepNow wrote:

sud21 wrote:a is equal to one of the numbers 5/11 , 7/12 , 9/13 , what is the value of a?

1) 5/11 < a < 3/4
2) 11/13 > a > 1/2

Target question: What is the value of a?

One approach is to write the APPROXIMATE decimal equivalents of each fraction.
We'll use a technique described in this free video (starting at 4:20 in the video): https://www.gmatprepnow.com/module/gmat- ... video/1073

5/11: if we multiply top and bottom by 9, we get 45/99, which is close to 45/100, which equals 0.45
7/12: if we multiply top and bottom by 8, we get 56/96, which is close to 56/100, which equals 0.56
9/13: if we multiply top and bottom by 8, we get 72/104, which is close to 72/100, which equals 0.72


Statement 1: 5/11 < a < 3/4
In other words, 0.45 < a < 0.72
So, a could equal 7/12 or 9/13
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: 11/13 > a > 1/2
In other words, 0.72 > a > 0.50
So, a could equal 7/12 or 9/13
So, a MUST equal 7/12
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

There seems to be an error with your statement 2 analysis.
11/13 is not equal to 0.72

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem.
Remember equal number of variables and independent equations ensures a solution.

a is equal to one of the numbers 5/11 , 7/12 , 9/13 , what is the value of a?
1. 5/11 < a < 3/4
2. 11/13 > a > 1/2

In the original condition there is 1 variable (a) and thus we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D has high probability of being the answer.

1) a=7/12, 9/13 noy suffi because not unique
2) a=7/12, 9/13 noy suffi because not unique
1) & 2) a=7/12, 9/13 noy suffi because not unique. therefore the answer is E

Normally for comparing fractions, we use cross methods. In other words, 5/11<7/12 --> cross-multiplying leads to 5*12<7*11 therefore the inequality sign is correct. Same goes for 9/13<3/4 --> 9*4<13*3

Normally for cases where we need 1 more equation, such as original conditions with 1 variable, or 2 variables and 1 equation, or 3 variables and 2 equations, we have 1 equation each in both 1) and 2). Therefore D has a high chance of being the answer, which is why we attempt to solve the question using 1) and 2) separately. Here, there is 59 % chance that D is the answer, while A or B has 38% chance. There is 3% chance that C or E is the answer for the case. Since D is most likely to be the answer according to DS definition, we solve the question assuming D would be our answer hence using 1) and 2) separately. Obviously there may be cases where the answer is A, B, C or E.

Math Revolution : Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World's First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Unlimited Access to over 120 free video lessons - try it yourself (https://www.mathrevolution.com/gmat/lesson)
See our Youtube demo (https://www.youtube.com/watch?v=R_Fki3_2vO8)