Hi Hesham,
Here is the most powerful strategy in data sufficiency: If you have to solve for any of "n" unknowns, you require "n" number of linear distinct equations.
So, if a word problem gave you three unknowns, you would need three linear distinct equations. Let's say the unknowns are x, y, and z. And then, say, I told you x=5. This is an equation (because it has an equal sign). But is it sufficient to solve for y or z? Nope.
Now, let's say I told you z = 10. So, now we know that x = 5 and z = 10. Clearly, we know what x and z are. But can we solve for y with these two equations? Of course not: y is still unknown!
Because there are three unknowns, we would need three equations to solve for the value of any of the unknowns.
If you know this, then it can really decrease the difficulty of a lot of DS questions. In fact, you can use this strategy even if you don't know
what an equation is; all you need to know is that there
is an equation, and the number of unknowns.
Let's apply the strategy to this problem:
In a certain country, the retail price include a value added tax of 12 1/2 percent of the sum of the whole cost and the mark up of an item. If the value added tax on a certain jacket is 6 shillings, what is the wholesale cost of the tax in shillings ?
A) The mark-up represents 50 percent of the wholesale cost.
B) The mark-up of the jacket is 16 shillings.
Let's translate the English sentence into an algebraic sentence. When translating, know the important terms, go slow, and chunk it up.
We learn that retail price INCLUDES a tax. Includes is not the same as EQUAL. "Retail price" is a red herring here.
The rest of the first sentence gives us English for the tax equation. The tax (let's call tax T) is equal to: 12 1/2 percent of the
sum of the
whole cost and the
mark up of an item.
We don't know the whole cost (so, let's call it WC) or the mark-up (so, let's call it MU). These are 2 unknowns.
The question is asking for WC (but it wouldn't have made a difference had the question been asking for MU).
The tax is 12.5 percent of the
sum of those two unknowns.
So, what is their sum? WC + MU
We have to take 12.5 percent
of this.
"of" usually means multiply in word problems:
Tax = 12.5%*(WC + MU)
We are told the tax was 6 shillings:
6 = 12.5% (WC + MU)
How many equal signs there?..1
And, how many unknowns (ie, letters) there?...2
We have one equation and two unknowns.
We will have sufficiency if we get an equation relating either WC or MU to a quantity (so long as there isn't a brand new unknown!)
We will have sufficiency if a statement gives us a value for WC or MU.
We will also have sufficiency if we get a special equation relating WC and MU.
ONLY now, after this analysis, are we ready to go to the statements.
Statement 1:
The mark-up represents 50 percent of the wholesale cost.
MU = 0.5*WC
So, in the original equation, we can replace "MU" with "0.5WC" and we would have sufficiency.
Of course, because it is data sufficiency we don't actually do that; we just know that we COULD do that.
Statement 1 is sufficient.
Statement 2 provides us with a value for one of our unknowns. Sufficient.
Choose D
Now, because it is data sufficiency, we didn't even have to write the original equation. We could just have noted that we had an equation relating tax to two unknowns, and said to ourselves: "I am in a one-equation and two-unkowns problem."
