Alright, I'm having a problem that is exacerbated by my current tests. I repeatedly run into problems where I am fully, 100% capable of solving the problem 'algebraically,' but am unable to solve it in practice because the arithmetic gets daunting. In these cases, I look at the explanations offered by my Test Prep software, and it is completely unhelpful since it almost completely appears to rely on either me using a calculator, or being a calculator.
An example of a problem that I know how to solve logically, but cannot work out the arithmetics of in a 2 minute time-frame. If someone could please tell me how I can effectively solve this problem I would really appreciate it:
Question: (Barron's GMAT Test Prep software, CAT #1)
Joan started work 2 years ago. Her starting salary was 1/2 of Mike's salary at that time. Each year since then Joan has received a raise of 5 percent in her salary and Mike has received a raise of 10% in his salary. What percentage (to the nearest percent) of Mike's current salary is Joan's current salary?
When I clicked on the explanation, I was offered this (skipping the verbal explanation):
JS = Joan's starting salary. JC = Joan's current salary.
MS = Mike's starting salary. MC = Mike's current salary.
MC = (1.10)(1.10)MS = (1.21)MS
JC = (1.05)(1.05)JS = (1.1025)JS
So,
JC = (1.05^2)JS = (1.1025)JS = .5(1.1025)MS = .55125[1.1/(1.1^2)]MC = (.55125/1.21)MC
Since we want the answer to the nearest percent, we must divide to three decimal places.
So .55125/1.21=.455, which is 46% to the nearest percent.
My problem:
I understand all the algebra behind this problem. It is difficult (though doable) for me to calculate that 1.05 squared is 1.1025, however, it is near impossible for me to calculate that .55125 / 1.21 = .455 . In fact, that latter problem would take me an eternity to solve by hand.
How can I solve this problem without really tedious calculations? It seems like I am doomed to fail these problems every single time because my brain is not wired like a calculator. If someone could show me an alternate way to solve this problem, or a proper way to solve the math by hand (.55125/1.21), I would really appreciate it.
-JV
An example of a problem that I know how to solve logically, but cannot work out the arithmetics of in a 2 minute time-frame. If someone could please tell me how I can effectively solve this problem I would really appreciate it:
Question: (Barron's GMAT Test Prep software, CAT #1)
Joan started work 2 years ago. Her starting salary was 1/2 of Mike's salary at that time. Each year since then Joan has received a raise of 5 percent in her salary and Mike has received a raise of 10% in his salary. What percentage (to the nearest percent) of Mike's current salary is Joan's current salary?
- 45
- 46
- 48
- 50
- 220
When I clicked on the explanation, I was offered this (skipping the verbal explanation):
JS = Joan's starting salary. JC = Joan's current salary.
MS = Mike's starting salary. MC = Mike's current salary.
MC = (1.10)(1.10)MS = (1.21)MS
JC = (1.05)(1.05)JS = (1.1025)JS
So,
JC = (1.05^2)JS = (1.1025)JS = .5(1.1025)MS = .55125[1.1/(1.1^2)]MC = (.55125/1.21)MC
Since we want the answer to the nearest percent, we must divide to three decimal places.
So .55125/1.21=.455, which is 46% to the nearest percent.
My problem:
I understand all the algebra behind this problem. It is difficult (though doable) for me to calculate that 1.05 squared is 1.1025, however, it is near impossible for me to calculate that .55125 / 1.21 = .455 . In fact, that latter problem would take me an eternity to solve by hand.
How can I solve this problem without really tedious calculations? It seems like I am doomed to fail these problems every single time because my brain is not wired like a calculator. If someone could show me an alternate way to solve this problem, or a proper way to solve the math by hand (.55125/1.21), I would really appreciate it.
-JV
