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21 Apr 2020, 04:42
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Hello abaisla,
It’s good that you have gone through the videos and are trying to apply your learnings in these questions. However, do not try to take the literal meaning out of a rule. What we mean by advising students to try all types of numbers is to tell them not to stick to one kind of values.
However, that does not mean that you have to try fractions in a question where integers have already helped you to disprove the statements. If integers have already done the job, why would you want to try fractions? Isn’t that a waste of your precious time? Think about it.
In question #2, we are trying to ascertain if b is even.
From statement I alone, 3a + 5b is even. Just by trying integer values here, I’m able to prove that b could be odd or even; thereby, I have already proved that the data given in the statement is insufficient. Now, having proved it insufficient, why will I waste time testing fractions again? Something to think about, isn’t it?
From statement II alone, 3a + 4b is even. From this, if we take integral values, we can only prove that a is even. However, for integral values, b could be odd or even. Statement II alone is already insufficient.
The bottom line is – you DON”T HAVE TO test fractions to prove the statements insufficient here.
However, since you have asked that question, let’s look at what fractions will work.
If a = \(\frac{1}{3}\) and b = \(\frac{1}{5}\), 3a + 5b = even but b is not even an integer, so how can it be even!
If a = 2 and b = 2, 3a + 5b = even and b is even.
Statement I alone is insufficient.
If a = \(\frac{1}{3}\) and b = ¼, 3a + 4b = even but b is not even.
If a = 2 and b = 2, 3a + 5b = even and b is even.
Statement II alone is insufficient.
When we combine both the statements, we see that only the integral values are the values that commonly satisfy both statements. The fractional values can be ruled out.
So, along with the rules of the game, you will also have to bring your prudence into action while solving problems. After all, every problem is unique and you can’t have a set of rules for each problem you solve. That is why you always have a fixed set of rules in every subject and using them in the right way is usually left to the student’s interpretation. As such, don’t fixate yourself on the rules. The question you are solving should drive the solution, not the rules.
Hope that helps!
It’s good that you have gone through the videos and are trying to apply your learnings in these questions. However, do not try to take the literal meaning out of a rule. What we mean by advising students to try all types of numbers is to tell them not to stick to one kind of values.
However, that does not mean that you have to try fractions in a question where integers have already helped you to disprove the statements. If integers have already done the job, why would you want to try fractions? Isn’t that a waste of your precious time? Think about it.
In question #2, we are trying to ascertain if b is even.
From statement I alone, 3a + 5b is even. Just by trying integer values here, I’m able to prove that b could be odd or even; thereby, I have already proved that the data given in the statement is insufficient. Now, having proved it insufficient, why will I waste time testing fractions again? Something to think about, isn’t it?
From statement II alone, 3a + 4b is even. From this, if we take integral values, we can only prove that a is even. However, for integral values, b could be odd or even. Statement II alone is already insufficient.
The bottom line is – you DON”T HAVE TO test fractions to prove the statements insufficient here.
However, since you have asked that question, let’s look at what fractions will work.
If a = \(\frac{1}{3}\) and b = \(\frac{1}{5}\), 3a + 5b = even but b is not even an integer, so how can it be even!
If a = 2 and b = 2, 3a + 5b = even and b is even.
Statement I alone is insufficient.
If a = \(\frac{1}{3}\) and b = ¼, 3a + 4b = even but b is not even.
If a = 2 and b = 2, 3a + 5b = even and b is even.
Statement II alone is insufficient.
When we combine both the statements, we see that only the integral values are the values that commonly satisfy both statements. The fractional values can be ruled out.
So, along with the rules of the game, you will also have to bring your prudence into action while solving problems. After all, every problem is unique and you can’t have a set of rules for each problem you solve. That is why you always have a fixed set of rules in every subject and using them in the right way is usually left to the student’s interpretation. As such, don’t fixate yourself on the rules. The question you are solving should drive the solution, not the rules.
Hope that helps!
