Thank you very much for your question. I’m very glad to know that you have come to a question-answer website to solve your problem. That means, you have a strong will to learn this math.  I really appreciate it. Thank you again.

Your question is – If the sum of 5 consecutive numbers is equal to 15 and the average of first three numbers is twice less than the average of the last three numbers, find the value of the third number in the series. It is given that the average of the last three numbers is 4.

Your Correct answer: d

I have solved this problem thus, you can read my Explanation for your better understanding:

According to the question,
The sum of five consecutive numbers = 15 …..i
And the average of last three numbers = 4 …..ii
The average of first three numbers = average of last three numbers – 2
Hence, the average of first three numbers = 4 – 2 = 2 …..iii
Hence, the sum of first three numbers = 2(3) = 6 …..iv
And, the sum of last three numbers = 4(3) = 12 …..v
Thus, the value of the third number in the series = (i) – (iv) – (v) = 15 – 6 – 12 = -3
Hence, the correct answer is option d.

If you have more question, ask me.

Thanks for asking question on GMAT Section,

Your question was – If x* = (3x + 2)/6, and x = 6x + 1, then what will be the value of x*?

Your correct answer is- A

Now read this explanation for more clarifications:

According to the data given in the question,
x* = (3x + 2)/6…..(i)
and x = 6x + 1……(ii)
Substituting the value of x from equation ii in equation i, we get,
x* = (3(6x + 1) + 2)/6
∴ x* = (18x + 3 + 2)/6
∴ x* = (18x + 5)/6
∴ x* = 3x + 5/6
Hence, the correct answer is option a.

Thanks for asking question on GMAT Section,

Your question was – What will be the square of x + 1/x, if it is given that x2+1/x2 = 34?

Your correct answer is- C

According to the data given in the question, x2+1/x2 = 34
We have to find the value of x+1/x
We have the standard algebraic formula for the square of addition of two numbers as
follows:
(a + b)2 = a2 + 2ab + b2
∴ (a + b)2 – 2ab = a2 + b2
Now substituting a =x and b = 1/x in the above formula, we get,
(x + 1/x)2 = 34 + 2*x*1/x
∴ (x + 1/x)2 = 34 + 2 = 36
Now taking square root on both the sides we get,
x + 1/x = ± 6
Hence, the correct answer is option c.

Thanks for asking question on GMAT Section,

Your question was – If (m + n) = 24, and the product of m and n is equal to 15, then find the value of the sum of the squares of the twovariables ‘m‘ and ‘n’.Alsofind the value of (m-n)2.

Your correct answer is- C

Now read this explanation for more clarifications:

According to the data given in the question,
(m + n) = 24…..(i)
m*n = 15……(ii)
We have to find the sum of the squares of the two variables ‘m’ and ‘n’ i.e. m2 + n2
According to the standard mathematical formula,
(m + n)2 = m2 + 2mn + n2……(iii)
∴ (m + n)2 – 2mn = m2 + n2……..(iv)
Substituting the value of m + n from equation (i) and (ii), in equation (iv), we get
(24)2 – 2(15) = m2 + n2
∴ 576 – 30 = m2 + n2
∴ m2 + n2 = 546
We also have to find the value of (m – n)2
Now, according to the standard mathematical formula,
(m – n)2 = m2 – 2mn + n2
∴ (m – n)2 = 546 – 2(15)
∴ (m – n)2 = 546 – 30 = 516
Hence, the correct answer is option c.

Thanks for asking question on GMAT Section,

Your question was –Which of the following statements hold true for writing as well as reading of the roman numbers?

i. You should always work from right to left in order to find the correct value of a roman number
ii. While moving from right to left, we add the values of the symbols when a lower value symbol is followed by a higher value symbol
iii. While moving from right to left, we subtract the lower value from the higher value, when a higher value symbol is followed by a lower value symbol
iv. There is no symbol to symbolize zero using the roman numbers
e. i and ii are true
f. ii and iii are true
g. I, ii and iii are true
h. None of the statements is true
i. All the statements are true

Correct answer: e

e. i and ii are true

Thanks for asking question on GMAT Section,

Your question was – Find out which of the following number is not a perfect square.

Your correct answer is- A

Now read this explanation for more clarifications:

According to the standard properties of square numbers, all perfect square numbers must end in either 0, 1, 4, 5, 6 or 9.
Now, looking at the given options, we find that options b, c and d have 4 and 5 as the digit in the unit’s place.
Hence, these numbers belong to the set of perfect squares.
Thus, we are left only with the option a. this number has 7 as the digit in the unit’s place.
Hence, it 2187 is not a perfect square.
Hence, the correct answer is option a.

Thanks for asking question on GMAT Section,

Your question was – Which of the following statements are true with respect to the properties of squares of any number?

Your correct answer is- E

Now read this explanation for more clarifications:

All the statements represent some or the other property that is possessed by the square numbers.
Hence, the correct answer is option e.

Thanks for asking question on GMAT Section,
Your question was – How will you represent the number 1600 with the help of roman numbers?
Your correct answer is- B

Now read this explanation for more clarifications:

According to the roman number representation scheme,
Letter I represents a value of 1
Letter X represents a value of 10
Letter V represents a value of 5
Letter L represents a value of 50
Letter C represents a value of 100
Letter D represents a value of 500
Letter M represents a value of 1000
We have to find the roman symbol for number 1600.
1600 = 1000 + 500 + 100 = M C D
Hence, the correct answer is option b.

You can also visit my website – http://knowledgeworldbd.com/

Thanks for asking question on GMAT section,

Your question was – What value does the roman number MCDL represent?

Your correct answer is- C

Now read this explanation for more clarifications:

According to the roman number representation scheme,
Letter I represents a value of 1
Letter V represents a value of 5
Letter X represents a value of 10
Letter L represents a value of 50
Letter C represents a value of 100.
Letter D represents a value of 500
Letter M represents a value of 1000

Here, We have to find the value represented by the roman symbol MCDL.
From the above data we can substitute the values for the respective symbols as follows,
M = 1000, C = 100, D = 500, L = 50
∴ MCDL = 1000 + 100 + 500 + 50
But, since, the value of C is less than the value if D, hence, we will subtract the value of C
from the value of D.
∴ MCDL = 1000 + (500 – 100) + 50 = 1450
Since, none of the options represent this value the correct answer is option e.
Hence, the correct answer is option e.

Thanks for asking question on GMAT section,

Your question was – In order to represent higher numbers with the help of roman symbols, a bar is placed on the top of the roman numbers and then the resultant number is multiplied by which of the following number to find out the exact value?

Your correct answer is- C

Now read this explanation for more clarifications:

According to one of the properties of Roman numbers, bar over the top of a roman

number indicates multiplication by 1000.

Hence, the correct answer is option c.