Basic Quantitative Example Question-01:
Many people start plugin values in such sort of questions, i.e. they start supposing some values and simply plugin in to see which one give an odd. But we strongly recommend to avoid plugin as much as you can, because plugin some values gives specific result (i.e. perhaps odd), but plugin some different might give a different result (i.e. perhaps even). For instance,
Question:
If a, b and c are consecutive integers, which of the following MUST be odd?
A) a + b + c
B) a + c
C) ab
D) abc
E) ab + 1
By putting a = 1, b = 2 and c = 3, the sum of a, b and c would be 6 (i.e. even). Is that mean the sum of any three consecutive integers always an even? No!
For instance, by putting a = 2, b = 3, and c = 4, the sum of the tree consecutive integers would become 9 (i.e. odd). That’s why we suggest to avoid plugin as much as you can, and instead simply think logically and remember the relationship of evens and odds as mentioned in the table of arithmetic operations with evens and odds.
Below is the method to solve such problems:
Solution:
It is given that a, b and c are consecutive integers, and we know that for any two consecutive integers, one of them must be even and the other one must be odd. But we cannot tell whether the first of those is even or odd. So we need to imagine both of the scenarios in mind (i.e. i. consider first of the three consecutive integers as even and ii. consider the first integer as odd) as below:
- If we consider a as even, then b must be odd and c must be even.
- If we consider a as odd, then b must be even and c must be odd.
According to first scenario, a + b + c would be odd, while according to second scenario, its sum would be even. Thus, Choice A is not MUST be odd.
Similarly, there are two scenarios for second choice:
- Both a and c are even.
- Both a and c are odd.
According to both scenarios, the result would always be even. Thus, Choice B is CANNOT be odd.
There’s only one possible scenario for third choice, i.e. the product of any two consecutive integer is always an even. This is because either of the two consecutive integers (i.e. a or b) is even. So the product of a and b would always be even. Thus, Choice C is CANNOT be odd.
Similarly, fourth choice would also result to even because three consecutive integers always include at least one even integer, so their product would always be even. Thus, Choice D is CANNOT be odd.
Finally, we have left with choice E, which must be the correct answer. Because the product of two consecutive integers (i.e. ab) always gives even, so even + odd (i.e. ab + 1) is always odd. Thus, Choice E MUST be an odd.
Note that, such way of solving (i.e. by applying logical thinking rather than plugin) seems very tedious and tiresome. But trust me, it is tiresome at initial stage. When you get used to with such way, you would become expert enough that you can simply see the question and answer while doing such things in your mind quickly. And never have any question incorrect.
In order to see another example, click on the “Example Question-02” button below: