If a is less than b, which of the following numbers is greater than a and less than b ?
(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a
which of the above options is the correct answer based on your calculation?
i don't seem to get any right
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The question stem should read as follows:
(A) (a + b)/2 --> (0+1)/2 = 1/2.
(B) ab/2 --> (0*1)/2 = 0.
(C) b² - a² --> 1² - 0² = 1.
(D) ab --> 0*1 = 0.
(E) b - a --> 1-0 = 1.
Eliminate B, C, D and E, which do not yield values between a=0 and b=1,
The correct answer is A.
Test a=0 and b=1 in the answer choices:If a is less than b, which of the following expressions MUST BE greater than a but less than b?
(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a
(A) (a + b)/2 --> (0+1)/2 = 1/2.
(B) ab/2 --> (0*1)/2 = 0.
(C) b² - a² --> 1² - 0² = 1.
(D) ab --> 0*1 = 0.
(E) b - a --> 1-0 = 1.
Eliminate B, C, D and E, which do not yield values between a=0 and b=1,
The correct answer is A.
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Hello Roland. I hope you're well.
You can pick two numbers and try option by option. Let's take a=1 and b=2. Now,
$$Option\ E:\ b-a=2-1=1,$$ this is not greater than a. INCORRECT.
$$Option\ D:\ ab=1\cdot2=2,$$ this is not less than b. INCORRECT.
$$Option\ C:\ b^2-a^2=2^2-1^2=4-1=3,$$ this is not less than b. INCORRECT.
$$Option\ B:\ ab/2=1\cdot2/2=1,$$ this is not greater than a. INCORRECT.
$$Option\ A:\ (a+b)/2=(1+2)/2=3/2=1,5,$$ this is greater than a and less than b. CORRECT.
So, the correct option is A.
I hope this can help you.
I'm available if you'd like any follow up.
Regards.
You can pick two numbers and try option by option. Let's take a=1 and b=2. Now,
$$Option\ E:\ b-a=2-1=1,$$ this is not greater than a. INCORRECT.
$$Option\ D:\ ab=1\cdot2=2,$$ this is not less than b. INCORRECT.
$$Option\ C:\ b^2-a^2=2^2-1^2=4-1=3,$$ this is not less than b. INCORRECT.
$$Option\ B:\ ab/2=1\cdot2/2=1,$$ this is not greater than a. INCORRECT.
$$Option\ A:\ (a+b)/2=(1+2)/2=3/2=1,5,$$ this is greater than a and less than b. CORRECT.
So, the correct option is A.
I hope this can help you.
I'm available if you'd like any follow up.
Regards.
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Let's let a = 3 and b = 4 and test each answer choice:BTGmoderatorRO wrote:If a is less than b, which of the following numbers is greater than a and less than b ?
(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a
which of the above options is the correct answer based on your calculation?
i don't seem to get any right
A) (a + b)/2 = (3 + 4)/2 = 3.5
We see that (a + b)/2 is greater than a and less than b.
We could stop here, but let's double-check the remaining answer choices.
B) ab/2 = 3(4)/2 = 6
We see that ab/2 is greater than b.
C) b^2 - a^2 = 16 - 9 = 7
We see that b^2 - a^2 is greater than b.
D) ab = 3(4) = 12
We see that ab is greater than b.
E) b - a = 4 - 3 = 1
We see that b - a is less than a.
The only answer choice that produced a value between a and b is A.
Alternate solution:
We are looking for a number that is between the two numbers a and b. We see that (a + b)/2 is the average of the two numbers and the average of any two numbers is always between the two numbers.
Answer: A
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If a and b are DIFFERENT numbers, then the average of a and b will always be BETWEEN a and bBTGmoderatorRO wrote:If a is less than b, which of the following numbers is greater than a and less than b ?
(A) (a + b)/2
(B) ab/2
(C) b^2 - a^2
(D) ab
(E) b - a
Since we're told a < b, we know a and b are DIFFERENT.
So, their average, (a +b)/2 must be BETWEEN a and b
Answer: A
Cheers,
Brent