How should my approach be to these kind of problems?

[golu23]

At a certain college there are twice as many English majors as History majors and three times as many English majors as Math's majors. What is the ratio of no of history majors to math's majors?
6:1,3:2,2:3,1:5,1:6

here's another one i tried by using smart nos but cant get it right and it keeps appearing on Gmat prep frequently

[chieftang]

There are three different types of majors in different ratios. Let's use 12 since it has numerous multiples.

Let E=12.

Then, H=6 and M=4.

So, H:M = 6:4 = 3:2

[Brent@GMATPrepNow]

At a certain college there are twice as many English majors as History majors and three times as many English majors as Math's majors. What is the ratio of no of history majors to math's majors?
6:1,3:2,2:3,1:5,1:6

Goal: Find the value of H:M

Let's set this up:
There are twice as many English majors as History majors: E:H = 2:1
There are three times as many English majors as Math's majors: E:M = 3:1

Notice that the common "bond" here is E - it will connect the required H and M terms.

In order to use the E to connect the H and M terms, we must make the two E values equal by creating equivalent ratios.

E:H = 2:1
Multiply both terms by 3 to get E:H = 6:3
Important step: If E:H = 6:3, then H:E = 3:6

E:M = 3:1
Multiply both terms by 2 to get E:M = 6:2

Now that the two E terms are equal, we can combine the ratios to get: H:E:M = 3:6:2
This means that H:M = 3:2

Cheers,
Brent

[gmatpup]

Sometimes I also have that issue where I think I picked smart numbers and they didnt work but once I try different numbers it works!

Here is what I did for this problem:

2x English than History - - Thus, (let's use 60 for English) so only 30 for History (60:30))
3x English than Math - - Thus, (we already have 60 for English so Math must be 20 (20:60))

Now, History to Math is 30:20, which is 3:2.

I hope this helps!!

[GMATGuruNY]

At a certain college there are twice as many English majors as History majors and three times as many English majors as Math's majors. What is the ratio of no of history majors to math's majors?
6:1,3:2,2:3,1:5,1:6

here's another one i tried by using smart nos but cant get it right and it keeps appearing on Gmat prep frequently

Plug in the SMALLEST NUMBER that is a MULTIPLE of all the DIVISORS.
Twice as many English majors means E should be a multiple of 2.
Three times as many English majors means E should be a multiple of 3.
The LCM (lowest common multiple) of 2 and 3 is 6.

Let E = 6.
Since there are twice as many English majors as history majors, H=3.
Since there are three times as many English majors as math majors, M=2.
H:M = 3:2.

The correct answer is B.

[chieftang]

LCM is probably the best approach to number picking here. But, let's face it, you don't even have to pick convenient numbers to get to the solution.

Let's pick a prime number like 7.

Let E=7.

Then, H=7/2 and M=7/3. This doesn't really make sense, unless we do creative counting for people who also have minor degrees. But it illustrates that to determine a ratio, the numbers you choose to plug in don't really make any difference.

So, H:M = 7/2:7/3 = 21/6:14/6 = 21:14 = 3:2


So, let's not even think of it as a number. Let's use a symbol.

Let E=ψ.

Then, H=ψ/2 and M=ψ/3.

So H:M = ψ/2:ψ/3 = 3ψ/6:2ψ/6 = 3ψ:2ψ = 3:2

[ArunangsuSahu]

Another Easy Way

E:H=2:1 or H:E=1:2

E:M=3:1

H:M=(H/E)*(E/M)=1/2*3/1=3:2

[golu23]

1) For every positive integer n, the function (n)his defined to be the product of all integers 2 to n inclusive, If p is the smallest prime factor of h(100)+1 then p is
a)Between 2-10
b)10-20
c)20-30
d)30-40
e)Greater than 40

In this question i figured out that the answer is "E" but wasn't able to solve it mathematically could someone please tell me how to do it.


2) Connie paid a sales tax of 8% on her purchase If the sales tax had been only 5% she would have paid 12$ less in taxes on her purchase. What was the total amount for her purchase including tax?
a)368
b)380
c)400
d)420
e)432.

For this problem tried many smart nos but i just couldn't figure it out.