Question 275 Data Sufficiency 2018 GMAT Official Guide
Question 275 Data Sufficiency 2018 GMAT Official Guide
Video explanation: If a and b are positive integers, is $\dfrac{a}{b} < \dfrac{9}{11}$...
Comments
Siemsays
Hi there,
First of all thanks for the videos, it is very helpful for my preparing for the test. I was wondering what type of method you use to do the divisions?
Hope to hear from you.
Could you elaborate on what you mean by divisions? Are you asking about arithmetic divisions? If that is the case then I always try to reduce numbers first, and only at the end will do the actual division. Most questions on the GMAT are written in a way that makes them amenable to arithmetic simplification by reducing terms.
A slightly different approach would be to rewrite the question in the main stem as: Is $9b > 11a$?
And then we can rephrase the given statement: $\displaystyle \frac{b}{a} > 1.223$ by multiplying both sides by $9$, which yields $9b > 11.007a$. This is given to us as a fact based on statement 2. If $9b$ is greater than $11.007a$, then we can certainly say that $9b > 11a$. Note that both $a$ and $b$ are positive. Therefore, statement 2 is sufficient.
In either of these approaches, division(more work) or multiplication(less work) has to be done to reveal the relationship.
Hi there,
First of all thanks for the videos, it is very helpful for my preparing for the test. I was wondering what type of method you use to do the divisions?
Hope to hear from you.
Could you elaborate on what you mean by divisions? Are you asking about arithmetic divisions? If that is the case then I always try to reduce numbers first, and only at the end will do the actual division. Most questions on the GMAT are written in a way that makes them amenable to arithmetic simplification by reducing terms.
I created a video here illustrating some basic steps of arithmetic simplification: https://mathquantum.com/strategy/arithmetic-manipulations/
Complicated method in Statement 2
Thanks for the comment.
A slightly different approach would be to rewrite the question in the main stem as: Is $9b > 11a$?
And then we can rephrase the given statement: $\displaystyle \frac{b}{a} > 1.223$ by multiplying both sides by $9$, which yields $9b > 11.007a$. This is given to us as a fact based on statement 2. If $9b$ is greater than $11.007a$, then we can certainly say that $9b > 11a$. Note that both $a$ and $b$ are positive. Therefore, statement 2 is sufficient.
In either of these approaches, division(more work) or multiplication(less work) has to be done to reveal the relationship.