Hey guys, I'm prepping for the Dec SAT and I think a daily math questions would help me improve. Can anyone help me with these questions? If you nee help too, feel free to post.
1. Kyle's lock combination consists of 3 two-digit numbers. The combination satisfies the three conditions below.
-One number is odd
-One number is a multiple of 5
-One number is the day of the month of Kyle's birthday
If each number satisfies exactly one of the conditions, which of the following could be the combination of the lock?
A. 14-20-13
B. 14-25-13
C. 15-18-16
D. 20-15-20
E. 34-30-21
I'm confused because A, B, and D all fit the conditions...
I'm not agreeing with how the question is given to us; but I'll give you the answer they're looking for.
The only thing you missed was the word "one." ONE number is odd. ONE number is a multiple of 5. And ONE number.. you get it.
A. 14-20-13
B. 14-25-13 - Eliminate because it has 2 odd numbers.
C. 15-18-16 - Eliminate because 15 can't satisfy two requirements.
D. 20-15-20 - Eliminate because it has two multiple of 5's.
E. 34-30-21 - Eliminate because 21 and 30 work, but 34 doesn't satisfy the birthday requirement.
The solution involves thinking of (p^2)(q) as p(pq). Since pq = 50, this is equal to 50p. All the answer choices are multiples of 50, but note that p must be a factor of 50, so 50p must be (a factor of 50) times 50.
200 is 50*4, and 4 is not a factor of 50, so C is the answer.
neatoburritoPosts: 3,019Registered UserSenior Member
That's a good example, rspence. The SAT loves the give you an expression and then tell you what a part of the factored form of the expression equals. They particularly like to do this with the difference of two squares and the occasional square of a sum or difference. The moral is, " If it can be factored, factor it." Or more colloquially, "Take it apart so that you can see more clearly what it's made of." It's a shame that schools tend to spend months teaching kids how to factor and little time explaining why you might want to do it.
Replies to: Daily Math Questions
The only thing you missed was the word "one." ONE number is odd. ONE number is a multiple of 5. And ONE number.. you get it.
A. 14-20-13
B. 14-25-13 - Eliminate because it has 2 odd numbers.
C. 15-18-16 - Eliminate because 15 can't satisfy two requirements.
D. 20-15-20 - Eliminate because it has two multiple of 5's.
E. 34-30-21 - Eliminate because 21 and 30 work, but 34 doesn't satisfy the birthday requirement.
A!
Here's another one I need help with:
Let x be defined as [x]=x^2-x for all values of x. If [a]=a-2, what is the value of a?
A. 1
B. 1/2
C. 3/2
D. 6/5
E. 3
Q: If p and q are positive integers such that pq = 50, which of the following cannot equal (p^2)q?
A: 50
B: 100
C: 200
D: 250
E: 500
[a] = a^2 - a = a - 2
a^2 - 2a + 2 = 0
a = (2 +- sqrt(4 - 8))/2, i.e. two complex solutions.
a^2 - a = (a-2)^2 - (a-2)
a^2 - a = a^2 - 5a + 6 (upon expanding, simplifying). a^2 cancels, leaving
-a = -5a + 6 --> a = 3/2
200 is 50*4, and 4 is not a factor of 50, so C is the answer.