GMAT Math Ratio Word Problems

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GMAT Math Ratio Word Problems

Hi Zeke,

I came acroos the following two problems, the two look similair but I think the approach is slightly different. Can you help me out please?

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In a certain calculus class, the ratio of the number of mathematics majors to the number of students who are not mathematics majors is 2 to 5. If 2 more mathematics majors were to enter the class, the ratio would be 1 to 2. How many students are in the class?

(A) 10

(B) 12

(C) 21

(D) 28

(E) 35

So let’s break this down sentence by sentence.

Step 1) Translate into math.
“the ratio of the number of mathematics majors to the number of students who are not mathematics majors is 2 to 5″

OK, so what do we know from this info?
Let’s use x and y.
X = # of math majors.
Y = # of non-math majors.

So it says the ratio of math to non-math is 2:5.
Now translate that.
“# of math to non-math” = x/y
2:5 translates = 2/5

so
x          2
–   =    —-
y          5

Cross multiply and you get:
(Equation #1) 5x = 2y

Step 2) Translate into math.
“If 2 more mathematics majors were to enter the class, the ratio would be 1 to 2.”

Instead of (x/y), we now do ((x+2)/y)
Instead of (2/5), we now do (1/2)
x+2          1
—-    =   —–
y             2

Cross Multiply and you get:
2(x+2) = 1(y)
(Equation #2) 2x + 4 = y
Combine this with (Equaiton #1) 5x=2y from above.
Notice (Equation 1) is 2y, which is twice the total amount in (Equation #2).
So all you have to do is double (Equation #2) so it matches (Equation #1).

2x +4 = y
becomes
4x + 8 = 2y
And equation (1) is 5x = 2y.

Step 3) Combine.
Now you see they both equal 2y, so you can just set the left hand side equal to each other

4x + 8 = 5x
8= x
x= 8
Now plug in x into (2x+4) = y; (2(8)+4) = 20 = y

So x = 8 and y = 20.
The total number of students is # of math + # of non-math, which is x + y = 8 + 20 = 28

So that’s an answer choice D. Voila!

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1. soaringAlone
  
  How about below approach ? Is there something wrong in it, I feel this is fast
  
  Ratio 2/5, lets assume
  
  1)maths majors=2k
  2)non maths major=5k
  3)total no of students=7k
  
  2 new entry in maths major- 2k+2
  
  (2k+2)/5k =1/2, solving for k gives k=4
  
  Total students from equation 3) above–7k=28.
2. kgb
  
  i like the second approach .
  kgb
3. M Rai
  
  Hi, you can solve this by plugging in each answer choice.
  To get a ratio 2:5, the total should be divisible by 7. (because 2+5=7).
  Answer choices A and B not divisible by 7. Hence, you can eliminate a and b. .
  Start with C.
  C: Total =21 => Ratio 1 is 6:15, add 2 to math, Ratio 2 is 8:15 => eliminate
  D: Total =28 => Ratio 1 is 8:20, add 2 to math, Ratio 2 is 10:20 => 1:2 =>Bingo. Answer is D.