GMATprep - Practice Test 1 => Have some problems figuring out right answers...

[GMAT n00b]

Dear GMAT professionals,
I did the first GMATprep Practice test and scored 650. When reviewing my mistakes, I still couldn't figure out the answers to all of the questions. I hope that you can help me and I hope that my questions aren't too stupid!


#1
If 5^21 * 4^11 = 2 * 10^n what is the value of n?
The answer is 21.

What I tried to do:
5^21 * 4^11 = 5^11 * 5^10 * 4^11 = 20^11 * 5^10. But then I got stuck...

#7
In isoceles RST what is the measure of <R?
(1) The measure of <T is 100°
(2) The measure of <S is 40°
The answer is Statement 1 alone is sufficient but 2 is not.

Is this the answer because we don't know which of the two angles are the same? Statement 1

states that T is 100 that means that R and S are the same and therefore 40 each? Statement

2 states that S is 40 but we do not know whether one of the two other angles is also 40?

#17
Is the integer k divisible by 4?
(1) 8k is divisible by 16
(2) 9k is divisible by 12
Answer is Statement 2 alone is sufficient.

I plugged in several integers for k and found out that 8k is divisble by 16 for k=2 but in this case, k is not divisible by 4. None of the numbers I found for 9k/12 worked also for k/4 (e.g.3,8,...). Is there a more efficient way to solve this question than just plugging in numbers?

#18
If the operation [+-*/] (it is a strange symbol in the actual test) is defined for all

integers a and b by a [+-*/] b = a+b-ab, which of the following must be true for all integers a b c?
1) a[+-*/]b = b[+-*/]a
2) a[+-*/]0 = a
3) (a[+-*/]b)[+-*/]c = a[+-*/](b[+-*/]c)
Answer is all are true.

I really don't know how to solve this problem.

#24
To furnish a room in a model home, an interior decorator is to select 2 chairs and 2 tables from a collection of chairs and tables in a warehouse that are all different from each other. If there are 5 chairs in the warehouse and if 150 different combinations are possible, how many tables are an in the warehouse?
Answer is 6.

#28
If m, r, x, and y are positive, is the ratio of m/r = x/y?
(1) m/y = x/r
(2) (m+x)/(r+y)=x/y
Answer: Statement 2 is alone sufficient but statement 1 isn't.


#33
If p is a positive integer, what is the value of p?
(1) p/4 is a prime number
(2) p is divisible by 3
Answer: Both together are sufficient.

I found 12, but how can I be sure that 12 is the only existing integer that fulfills the two statements?


I would be really grateful if you could help me with my problems....

Thanks a lot!!!

[ace_gre]

Good questions...

Q1.
5^21 * 4^11 = 2 * 10^n.
5^21 * 2^22 = 2* 10^n
5 ^11 * 5 ^10 * 2^11 * 2^11= 2* 10^n.Cancel one 2 on either side
5^11* 5^10* 2^11*2^10=10^n Combine like powers of 5 and 2
5^11 * 2^11*5*10*2^10 =10^n
10^11*10^10=10 ^n
10 ^21=10^n
21=n.

Q7.
Sum of the interior angles of a triangle is 180. In a triangle only one angle can be greater than 100. This obviates the possibility of another angle measure of 100.
Hence I alone is sufficient.

Q17.
I)Express as factors of prime numbers.
8k=2*2*2*k.
16=2*2*2*2. Any number which is a multiple of 2 will satisfy the equation. 2,4,6,8,10,12,14, some of which are not divisible by 4.
II) Express as factors of prime numbers.
9k=3*3*k
12=3*2*2. 9k is divisible by 12 only when k is a multiple of 4..like 4,8,12,16...Hence k is divisible by 4.

Q18.
The symbol is daunting! May be you could replace with * and make it easier...
Rewriting a*b=a+b-ab.
1)a*b = a+b-ab, b*a=b+a-ba (identical)
2) a*0 = a +0-a x 0=a (identical)
3) (a*b)*c = (a+b-ab)*c. The whole term in the bracket is now like "a"
===> a+b-ab+c-(a+b-ab)c=a+b-ab+c-ac-bc+abc
Evaluate a*(b*c) in a similar way.Both sides are identical.

Q24.
Let the number of tables available x. No. of ways of selecting 2 out of 5 chairs is 5C2=10.
5C2* xC2 = 150
xC2= 15.

We already know that 5C2= 10. So try the next higher number..6 for x.
6C2=15. Hence the total no. of tables available is 6

Q28.
I)m/y=x/r
==>mr=xy (not sufficient)
11)(m+x)/(r+y)=x/y.
Cross-multiply,my+xy=rx+xy. Cancel xy on both sides and write as ratios,m/r=x/y. (II alone sufficient)

Q33.
I)p/4 = prime number. For this to be true,p has to be a multiple of 4 and a prime number. So it can be 2*4,3*4,5*4,7*4,11*4.....
II) states p is divisible by 3.So p=12 and no other number will satisfy this condition.

Hope this helps!

[GMAT n00b]

Wow, thanks a lot ace gre!!!
Your answers help me a lot!

[GMAT n00b]

I now understood all of the solutions but one.

#33
How can I be sure that 12 is really the only number that is a prime number if divided by 4 and that is also divisible by 3?
I understand that 12 is a number that fulfils both equations but how can I be sure that it is the only one?

[ritica]

#33

From the first statement we can write p=x*4 , where x is a prime number.
From second statement we know that p is divisible by 3 . Which means x must be a multiple of 3. Since x is prime no hence x=3. Thus p=3*4=12

I hope this explanation helps.