We generally see a lot of questions involving fractions and percents on the GMAT. The fact is that sometimes you will try a method to solve a question and that method does not work out to be the best way. Don’t give up! Try solving with another method. Of course, the best thing is to select the correct method from the word go, but really: This won’t work all the times on a test day for all the Quant questions. Be ready to change the track when required..!
Let’s just take a look at these below-given examples and try to solve creatively rather than getting stuck with most usual ways.
Consider the following problem:
A certain high school band consists of only fourth graders and fifth graders, of the members are fourth graders and remaining are fifth graders. If of the fourth graders play guitar and of the fifth graders play guitar, what fraction of all the members are not the guitarist?
The usual way to solve this GMAT question
The more usual way of doing this problem is to solve algebraically. The students start this question by taking a variable for the ‘unknown’ quantity i.e the total number of members in the band.
So, we’ll first see the algebraic way. Our first task: assigning a variable for the total number of members in the band.
Let it be x,
Then, no. of juniors = 3/5 x,
No. of juniors, who play guitar = (1/4)∗(3/5)x=3/20x
And, no. of seniors = 2/5x
No. of seniors, who play guitar = (2/3)×(2/5)x=4/15x
Total number of guitarist = 3/20x+4/15x=25/60x
Therefore, fraction of guitarist = 25/60=5/12
But, question asked about fraction of members who are not guitarist,
Hence answer is C.
The creative way to solve this GMAT question
The more creative way to solve this question is arithmetical. In this case, we take help of real numbers to solve this question. Solving this problem like a real world problem will definitely save time and efforts.
What should be a good number here to start? Let me tell you whenever there are fractions given, an easy number to start is simply the product of all the denominators of the fractions involved. Like in this case, there are 3, 4, and 5 in the denominator so, I am starting by taking their product i.e. 60.
So, let us assume total number of students to be 60
# of juniors is 3/5×60=36
no. of juniors, who play guitar = 1/4×36=9
# of seniors is 60 – 36 = 24 and no. of seniors, who play guitar = 2/3×24=16
So, total members who play guitar is 16 + 9 = 25 and total members who don’t play guitar is 60 – 25 = 35
Therefore, fraction of the members who do not play guitar is 35/60=7/12
Hence, the answer is C
The key take away from the above question:
1. The GMAC is least bothered about how you solve the question neither should you. Always involve creative thinking while solving.
2.Practice makes a man perfect. Practice enough “wordy” problems. By doing so you will feel comfortable in –
• executing best way outs
• knowing when it’s better for you to do algebra and when it’s better to do arithmetic, and
• Identifying whether the question should be done effectively & quickly by using algebra or arithmetic.