Please help with answers - Just took my 1st Prep Test - 540 - UGH

[LMK2727]

1. 5^21 * 4^11 = 2 * 10^n
   How does n = 21 ?!
   
2. For every positive integer n, the function h(n) is defined to be the product of all even integers from 2 to n inclusive. If p is the smallest prime factor of h(100) + 1, then p is?
   
   How is p great than 40?!
   
3. 1/3 pets are dogs and 1/5 of the pets are birds. There are 20 more dogs than birds.
   
   How do you work this out?!
   
4. If L and K are lines on an xy plane, is the product of the slopes of L and K = to -1?
   
   1. L passes through (1,2)
      
   2. K has x-intercept 4 and y intercept 2
   
   How is the answer C?
5. 2^x – 2^x-2 = 3(2^13) How does x = 9?!
   
6. y=(x+a)(x+b) Do they intercept at the x-axis?
   
   1. A+b=1
      
   2. Graph intersects at the y-axis at (0,-6)
   
   How is answer C?
   
7. M is a finite set of neg numbers, is the total number of integers in M an odd #?
   
   1. Product of all integers in M is odd
      
   2. Product of all integers in M is negative
   
   How is the answer B?
8. What is the value of h?
   
   1. H^2 =36
      
   2. H^2+12h = -36
   
   How is the answer B?
   
9. S & T are 2 different numbers on the number line. Is S + T = 0?
   
   1. Distance between S & 0 is the same as T & 0
      
   2. 0 is between S&T

How is the answer A?!

[chrisw123]

because im supposed to be working, i'll only do number 1. and i'll do the rest soon if no one else does.

5^21 * 4^11 = 2 * 10^n

10^n = 2^n x 5^n
and 2 = 2^1
and 4^11 = 2^11 x 2^11
and 2^11 x 2^11 = 2^22
AND 2^1 x 2^n = 2^n+1

So 5^21 x 2^22 = 2^n+1 x 5^n

just grabbing the exponents...
21 x 22 = n+1 x n

n = 21

And you can sorta see that really quickly from the start, its painful to write it all down

[chrisw123]

number 2 has been done solved on this board already - i never really understood it either, infact, i never really understood the question - and i never cared

number 3 quick way - choose a multilple of 15 - (because 1/3 dogs and 1/5 birds)
eg. 15 pets = 5 dogs, 3 birds... (2 more dogs)

says there is 20 more dogs - multiply it all by 10. = 150 pets, 50 dogs, 30 birds. there you go...

or slow way: 1/3P=D 1/5P=B D=B+20 (P-pets, D-dogs, B-birds)
Solve equations...
5/15P = 3/15P+20
2/15P=20
P=150

[chrisw123]

number 4 i dont get C

i get E

If L and K are lines on an xy plane, is the product of the slopes of L and K = to -1?

1. L passes through (1,2)
2. K has x-intercept 4 and y intercept 2

we need both slopes. 2 gives us K slope -1/2 . But 1 doesnt tell us L's slope, it could be 2, or anything else....

Whats wrong ?

[chrisw123]

umm number 5 is written wrong?

I get x = 15, not 9....

and i dont understand 6 - 'they' intersect? is there supposed to be two lines?

7 - M is a finite set of neg numbers, is the total number of integers in M an odd #?

1. Product of all integers in M is odd
2. Product of all integers in M is negative

1) Could be odd or even amount of numbers, eg. -1 or -1,-3
2) Must be an odd amount of numbers to have a negative result.

B ans.

8
What is the value of h?

1. H^2 =36
2. H^2+12h = -36

1) can be -6 or 6
2) =h^2+12h+36 = 0
= (x+6)(x+6) = 0
x = -6

ans is B again
(COMMON TRICK QUESTION)


and 9 - S & T are 2 different numbers on the number line. Is S + T = 0?

1. Distance between S & 0 is the same as T & 0
2. 0 is between S&T

Ans is A - Different numbers and same distance means 1 and -1, 4 and -4, etc.

B wrong because could be -1 and 3, which doesnt =0. or 2,-2 which does.

[LMK2727]

Thank you so much for the posts Chris!

Is there an easy way to get from: 21 x 22 = n+1 x n to n = 21? I'm missing the step inbetween.

[LMK2727]

#5: How did you get 15?!

[sruthi07]

because im supposed to be working, i'll only do number 1. and i'll do the rest soon if no one else does.

5^21 * 4^11 = 2 * 10^n

10^n = 2^n x 5^n
and 2 = 2^1
and 4^11 = 2^11 x 2^11
and 2^11 x 2^11 = 2^22
AND 2^1 x 2^n = 2^n+1

So 5^21 x 2^22 = 2^n+1 x 5^n

And you can sorta see that really quickly from the start, its painful to write it all down

just grabbing the exponents...
21 x 22 = n+1 x n...

once we take the like terms together, shdnt it be
5^21/5^n= 2^n+1/2^22?
taking the exponents,

21-n= (n+1)-22
=> 21-n = n+1 -22
21-n = n-21
2n = 2*21
=>n= 21

[solarisgirl]

chrisw123, can you elaborate on the last part? How does that n = 21?

just grabbing the exponents...
21 x 22 = n+1 x n

n = 21 ??

I get 462= n^2+n

or sruthi07, can you explain why we have to divide those terms?

5^21/5^n= 2^n+1/2^22?

[vnf]

5. 2^x – 2^x-2 = 3(2^13) How does x = 9?!

#5: How did you get 15?!

2^x - 2^x-2 = 3 (2^13)
2^x - 2^x/2^2 = 3 (2^13)
4 (2^x) - 2^x = 3 (2^13) 2^2
3 (2^x) = 3 (2^15)

=> x = 15