ERROR IN CAT

[GUEST]

Hello guys

I thing there are 2 errors in one of the CATs I have just done.
The first one is below :

Question 16 of 37

A certain NYC taxi driver has decided to start charging a rate of r cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?

A) 3xr/2

B) 3x/200r

C) 3r/200x

D) 3xr/200

E) xr/600

We can solve this as a VIC (Variable In answer Choices) and plug in values for x and r.
r
cents per person per mile
10

x
# of miles
20


Since there are 3 people, the taxi driver will charge them 30 cents per mile.
Since they want to travel 20 miles, the total charge (no discount) would be (30)(20) = 600.
With a 50% discount, the total charge will be 300 cents or 3 dollars.

If we plug r = 10 and x = 20 into the answer choices, the only answer that yields 3 dollars is D.

The correct answer is D.

This explanatin is wrong, I think. If solved algebraically, its quite simple to see that the answer is 3xr/2,as this is half of or with 50% off what 3 people should be paying for travelling x miles at 3r cents/mile. Correct answer I think is A.

2) This the 2nd question

Question 27 of 37

If Sq root (x+4)^2 = 3, which of the following could be the value of x - 4?
-11
-7
-4
-3
5
Square both sides of the given equation to eliminate the square root sign:
(x + 4)^2= 9 - I dont think this is right - Sq root (x+4)^2 = 3 MEANS (x+4)^2x0.5 = 3 which MEANS (x+4) = 3. COULD THE MODERATORS PLEASE HAVE A LOOK AT THIS ? Its just this type of basic thing that the GMAT loves to throw up. Thanks. The rest is the exoplanation.

Remember that even exponents "hide the sign" of the base,so there are two solutions to the equation: (x + 4) = 3 or (x + 4) = -3. On the GMAT, the negative solution is often the correct one, so evaluate that one first.
(x + 4) = -3
x = -3 - 4
x = -7

Watch out! Although -7 is an answer choice, it is not correct. The question does not ask for the value of x, but rather for the value of x - 4 = -7 - 4 = -11.

Alternatively, the expression can be simplified to |x + 4|, and the original equation can be solved accordingly.
If |x + 4| = 3, either x = -1 or x = -7

The correct answer is A.

You must select an answer to proceed.
© Copyright 2007 by MG Prep, Inc.

[esledge]

This explanatin is wrong, I think. If solved algebraically, its quite simple to see that the answer is 3xr/2,as this is half of or with 50% off what 3 people should be paying for travelling x miles at 3r cents/mile. Correct answer I think is A.

If we wanted the cost in cents, you would be right. You are forgetting the "How much, in dollars, ..." part of the question. This is part of the reason we recommend picking numbers: it's not that it's difficult to solve algebraically, it's just very easy to miss something when you are thinking abstractly. When you deal with numbers, you are much more likely to remember the cents-to-dollars conversion required by the language in the problem.

Square both sides of the given equation to eliminate the square root sign:
(x + 4)^2= 9 - I dont think this is right - Sq root (x+4)^2 = 3 MEANS (x+4)^2x0.5 = 3 which MEANS (x+4) = 3. COULD THE MODERATORS PLEASE HAVE A LOOK AT THIS ? Its just this type of basic thing that the GMAT loves to throw up. Thanks. The rest is the exoplanation.

On this one, you are forgetting the negative solution. Whenever there are variables under the square root sign, you must fall back on this property:

sqrt(x^2) = |x| {Not just x alone! There is a brief mention of this on p.126 of OG 11th edition}

The reason? Consider this example: sqrt(x^2) = 9
Following the rule, sqrt(x^2) = |x| = 9. Thus, x = 9 or -9. Plug back into the original to see that both are valid solutions.

Plugging x = 9 to check: sqrt(x^2) = sqrt(9^2) = sqrt(81) = 9
Plugging x = -9 to check: sqrt(x^2) = sqrt((-9)^2) = sqrt(81) = 9

[asharma8080]

Sorry to bring up this old one out of the grave in advance...

I came across the second problem ... which of the following could be the value of x - 4??

Why can not we do sqrt (x+4) ^ 2 = 3 = > (x+4) ^ (2/2) = 3 and then x + 4 = 3 and x = -1???

What am I missing here? I understand that we can square both sides and cancel out the sqrt but what is wrong about using the sqrt, which is essentially something raised to the power of 1/2, to cancel the square outside (x+4)?

FYI...I have read Emily's explanation a couple times but still not getting it...

[tim]

there's nothing to "get" about Emily's explanation. you just need to remember the rule that sqrt(a^2) = |a| and watch for this to happen in questions..