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If I saw this problem without thinking, I might multiply out the second column (3 times 10³ is 3000, etc). Such an approach is self-defeating. There is a simple trick here. Notice that 3569 is the same thing as saying 3000 + 500 + 60 + 9, which is what the expression on the right is really saying. Calculation is not necessary, and I know that both expressions are equal.
2. 31 x 32 x 33 x 34 x 35 OR 32 x 33 x 34 x 35 x 36
Again, if you don’t quickly examine the two expressions intelligently, you might jump into calculation, which would take you quite a while (not to mention leave you vulnerable to errors). Since we are just comparing the two expressions, we can cross out the numbers that appear in both expressions, that is, 32, 33, 34, and 35. Thus, we are left with a simple comparison: 31 OR 36; now it’s quite clear that B is greater.
Trick - Simplify
When presented with two baffling expressions, always think of ways to simplify before you calculate. Let’s check out this example:
1. 2,000,000 / 200, 000 OR 1,000 / 100
When you see many zeros in fractions like this, your first instinct should be to cross out matching zeros. If I have 2,000,000 in the numerator and 200,000 in the denominator, I should just eliminate five zeros from the top and 5 zeros from the bottom; now, my expression is simply 20/2 = 10. Same idea for column b: 1,000/100 = 10/1 = 10.
Simplify by Adding/Subtracting Same Value
1. 4x +5 OR 3x +6
I could approach this problem a few ways. First, I could use the tried and true plug-in method, where I would test a few simple numbers (preferably something like -2, 0, 2, and .5–you want to use a positive, a negative, 0, and a fraction). Don’t forget, though, that you can manipulate both expressions to make the comparison simpler. As long as I add or subtract the same number or variable from these expressions, I’ll have the same relationship between the two expressions. Remember, when choosing numbers to add or subtract, our goal is to make the relationship simpler, so:
Subtracting 5 from both sides gives us:
4x OR 3x+1
Subtracting 3x from both sides gives us:
x OR 1
Now, look how simple it is? The comparison is any number (x) OR 1, which is clearly indeterminate. Our answer is D.
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