1) After giving $5 to Greg, David has $25. Greg now has 1/5 as much as Davis does. How much did Greg start with?
2) if 3a+4b=4a-4b=21 find the value of a
A)3
B)6
C)21
D)42
E) the answer can not be determined from the information given
^ i think it’s C?
3) If N is a positive integer, which of the following does not have to be a divisor of the sum of N,6N, and 9N?
A)
B)2
C)4
D)9
E)16
^Is it D??
1) So Greg has 1/5 of 25, so he has $5. He was given $5 in the beginning, so at first he had 5-5=0 dollars
2) Subtract 3a from each side, ignoring the 21 for now:
4b=a-4b
Add 4b to each side
8b=a
Going back to the first equation, we have
3a+4b=21
Since a=8b, we can substitute
3(8b)+4b=21
24b+4b=21
28b=21
b=21/28=3/4
so b=3/4 and a=8b
8*b=8*3/4=24/4=6
answer is B
3)
N+6N+9N=16N
All the factors of 16 must be a factor of 16N, so 1, 2, 4, 8, and 16 are all factors. 9 does not have to be a factor, answer is D) 9
1) Let's solve question 1 step-by-step:
Let's assume Greg originally had x dollars.
After giving $5 to Greg, David has $25. This means David originally had 25 + 5 = 30 dollars.
Given that Greg now has 1/5 as much as David does, we can set up the equation:
x = (1/5) * 30
Simplifying the equation, we get:
x = 6
Therefore, Greg originally had $6.
2) Let's solve question 2 step-by-step:
Given equations:
3a + 4b = 21
4a - 4b = 21
To find the value of a, we can solve these equations by eliminating b.
Add the two equations:
(3a + 4b) + (4a - 4b) = 21 + 21
Simplifying the equation, we get:
7a = 42
Divide both sides of the equation by 7:
a = 6
Therefore, the value of a is 6. So the answer is B) 6.
3) Let's solve question 3 step-by-step:
We need to find which number does not have to be a divisor of the sum of N, 6N, and 9N.
The sum of N, 6N, and 9N is:
N + 6N + 9N = 16N
Now, let's check the given options one by one:
A) 2: If N is even, then 16N will definitely be divisible by 2. So, this option is not the answer.
B) 4: 4 divides all multiples of 4. Since 16 is a multiple of 4, 16N will always be divisible by 4. So, this option is also not the answer.
C) 9: For 9 to be a divisor of 16N, N would have to be a multiple of 9. But N is a positive integer, so we cannot guarantee that 16N will always be divisible by 9. Therefore, this option could be the answer.
D) 16: Since 16 is a factor in 16N, it is always divisible by 16. So, this option is not the answer.
Therefore, the answer is C) 9.
1) To solve this problem, we can set up an equation based on the given information. Let's assume Greg started with x dollars. After giving 5 dollars to Greg, David has 25 dollars. This can be expressed as:
x + 5 = 25
Simplifying this equation, we get:
x = 25 - 5
x = 20
Therefore, Greg started with 20 dollars.
2) In order to find the value of 'a', we need to solve the system of equations:
3a + 4b = 21
4a - 4b = 21
To eliminate 'b', we can add the two equations together:
(3a + 4b) + (4a - 4b) = 21 + 21
Simplifying this equation, we get:
7a = 42
Now, we can solve for 'a' by dividing both sides of the equation by 7:
a = 42/7
a = 6
Therefore, the value of 'a' is 6. The correct answer is option B.
3) To determine which of the options does not have to be a divisor of the sum of N, 6N, and 9N, we need to evaluate each option. Let's consider each option one by one:
A) If the sum is divisible by 'N', it is also divisible by 2, so this option is not correct.
B) If the sum is divisible by '2', it is also divisible by 4, so this option is not correct.
C) If the sum is divisible by '4', it is also divisible by 2, so this option is not correct.
D) If the sum is divisible by '9', it does not necessarily imply that it is also divisible by 4, so this option is correct.
E) The option '16' is not even considered in the given question, so we cannot determine if it is correct or not.
Therefore, the correct answer is option D, which is '9'.