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The average (arithmetic mean) of a and b is 90; the average (arithmeti
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16 Dec 2019, 23:09
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Competition Mode Question The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (bc)/2? A) 60 B) 120 C) 30 D) 60 E) 40
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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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16 Dec 2019, 23:24
\(\frac{a+b}{2}=90\) and so \(a+b=180\) \(\frac{a+c}{2}=150\) and so \(a+c=300\)
Subtracting the two,
\(a+bac=180300\) \(bc=120\) \(\frac{bc}{2}=60\)
Answer is (D)



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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 00:48
(a+b)/2 = 180 (a+c)/2=300
solving above we get (bc)/2=60
OA:D



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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 01:02
given a+b= 180 and a+c= 300 subtract bc= 120 so bc/2= 60 IMO D
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (bc)/2?
A) 60 B) 120 C) 30 D) 60 E) 40



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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 02:21
Quote: The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (bc)/2?
A) 60 B) 120 C) 30 D) 60 E) 40 a+b=90*2=180 a+c=150*2=300 bc=120 bc/2=120/2=60 Ans (D)



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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 02:55
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (bc)/2? A) 60 B) 120 C) 30 D) 60 E) 40 a + b = 180  Eqn. 1 a + c + 300  Eqn. 2 Eqn. 1  Eqn. 2 a + b  a  c = 180  300 b  c =  120 \(\frac{bc}{2} =  60\) Answer D.
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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 05:00
a+b = 180 a+c = 300  (Subtracting both equations) b  c = 120 \(\frac{(bc)}{2}\) = 60
IMO, D



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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 05:54
From the above,(a+b)/2=90, implies a+b=180.................(1) (a+c)/2=150, implies a+c=300..................(2) (1)(2)=> bc=120 Hence (bc)/2=60.
The answer is therefore D.



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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 15:09
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of \(\frac{(bc)}{2}\) ?
a+b =180 a+c =300 > a+ba c= 180300 > bc =120 > \(\frac{(bc)}{2} = \frac{120}{2}= 60\)
The answer is D.



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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 21:03
The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (bc)/2?
A) 60 B) 120 C) 30 D) 60 E) 40
Solution : a+b/2= 90 there fore a+b= 180 a+c/2=150 Therefore a+c=300
a+b=180  a+c=300 =bc=120
Therefor bc/2= 60
IMO D



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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 22:16
(a+b)/2 = 90.....(i) (a+c)/2 = 150.....(ii)
(i)  (ii) gives us: (a+bac)/2 = 90150 => (bc)/2 = 60
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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 06:36
Quote: The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (bc)/2? So, \(a + b = 180\) ; \(a + c = 300\) Now, \((a + b )  ( a + c ) = a  c\) Or, \(\frac{a  c }{2}= \frac{180  300}{2}\) Or, \(\frac{a  c }{2} = 60\), Hence, Answer must be (D) 60
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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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17 Dec 2019, 22:33
Bunuel wrote: Competition Mode Question The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (bc)/2? A) 60 B) 120 C) 30 D) 60 E) 40 OFFICIAL EXPLANATION Translate the question into algebra, using the formula that the average equals the sum of the terms divided by the number of terms. 90 = (a + b)/2 Multiply by 2: 180 = a + b 150 = (a + c)/2 Multiply by 2: 300 = a + c At this point, there are two ways to manipulate the algebra. Method 1Line up the two equations so that you can subtract them. Equation 1: a+b = 180 Equation 2: a+c = 300 Notice that the equations are lined up such that if you subtract them, you end up with bc on the left and a number on the right. Since you are trying to find (bc)/2, this setup will get you most of the way to the answer. Subtract the two equations: Equation 1: a+b = 180 Equation 2: a+c = 300 Equation 1  2: a  a + b  c = 180  300 = 120 Equation 1  2 (cont.): bc = 120 With bc = 120, if you divide by two, you arrive at the equation that you are being asked for: (bc)/2 = 120/2 = 60 Method 2Since the question asks for the value of (bc)/2, solve the two equations for the variable a so that they can be combined. a = 180 – b a = 300 – c Combine the two equations by setting them equal to each other (since a = a) and manipulate them such that (bc)/2 is on one side of the equation and a number is on the other. 180 – b = 300 – c 180 – 300 = b – c 120 = bc 60 = (b – c)/2
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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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21 Dec 2019, 20:08
Bunuel wrote: Competition Mode Question The average (arithmetic mean) of a and b is 90; the average (arithmetic mean) of a and c is 150; what is the value of (bc)/2? A) 60 B) 120 C) 30 D) 60 E) 40 We can create the equations: a + b = 180 and a + c = 300 Subtracting the second equation from the first, we have: (b  c) = 120 Therefore, (b  c)/2 = 120/2 = 60. Answer: D
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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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22 Dec 2019, 02:46
The average (arithmetic mean) of a and b is 90, this should translate to: (a + b)/2 = 90 => a + b = 180  (1) Similarly, a + c = 300  (2)
Now the question requires us to find (b  c), thus, subtract (2) from (1) & we will get: b  c = 120 divide both the sides by 2 to get the requisite value; (b  c)/2 = 60
Thus, the correct answer is D.
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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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02 Jan 2020, 15:07
\(\frac{(a+b)}{2}=90\) and \(\frac{(a+c)}{2}=150\) (a+b)=180 and (a+c)=300 \(a=180b\) and \(a=300c\) \(180b=300c\) \(b=180\) \(c=300\) \(\frac{(180300)}{2}=60\) Answer: D
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Re: The average (arithmetic mean) of a and b is 90; the average (arithmeti
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