If $p = a^{x} . b^{y} . c^{z}$ and $q = 3^{x} . b^{4} {.5}^{z}$ where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?

a = b = c

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x = y = z

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a = 3x

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a + c = 2y

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Solution

The correct option is D
a + c = 2y

Since the prime factorization of a number is UNIQUE, we must have a = 3, y = 4, c = 5.
Hence ruling out the options, we find that a+c = 3 + 5 = 8 = 2y is the correct answer.

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Similar questions

If $p = a^{x} . b^{y} . c^{z}$ and $q = 3^{x} . b^{4} {.5}^{z}$ where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?

If $a = p^{l} . q^{m} . r^{n}$ and $b = p^{x} . q^{y} . r^{z}$ where p,q,r are primes and p<q<r and l,m,n,x,y,z are all natural numbers. Given HCF = $p^{2}$ . $q^{3} . r$ and LCM = $p^{3}$ . $q^{4}$ . $r^{3}$ , which one of the following is NOT true?

If $a = p^{l} . q^{m} . r^{n}$ and $b = p^{x} . q^{y} . r^{z}$ where p,q,r are primes and p<q<r and l,m,n,x,y,z are all natural numbers. Given HCF = $p^{2}$ . $q^{3}$ .r and LCM = $p^{3}$ . $q^{4}$ . $r^{3}$ , which one of the following is NOT true?

Q. If

A = ⎡ ⎢ ⎣ \begin{matrix} a & b & c x & y & z p & q & r \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} q & - b & y - p & a & - x r & - c & z \end{matrix} ⎤ ⎥ ⎦

and if

A

is invertible, then which of the following is/are true:

Q. If

p, q, r, b, c

are non zero real numbers such that

p + q + r = 16

b + c = 4

, then find the value of

x + y + z

Where

x, y, z

satisfy the system of equations:

\frac{x}{p} + \frac{y}{p - b} + \frac{z}{p - c} = 1

\frac{x}{q} + \frac{y}{q - b} + \frac{z}{q - c} = 1

\frac{x}{r} + \frac{y}{r - b} + \frac{z}{r - c} = 1

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If p=ax.by.cz and q=3x.b4.5z where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?

The correct option is D a + c = 2y Since the prime factorization of a number is UNIQUE, we must have a = 3, y = 4, c = 5. Hence ruling out the options, we find that a+c = 3 + 5 = 8 = 2y is the correct answer.

If $p = a^{x} . b^{y} . c^{z}$ and $q = 3^{x} . b^{4} {.5}^{z}$ where a,b,c are primes and x,y,z are natural numbers, then which of the following is true if p=q ?

The correct option is D
a + c = 2y

Since the prime factorization of a number is UNIQUE, we must have a = 3, y = 4, c = 5.
Hence ruling out the options, we find that a+c = 3 + 5 = 8 = 2y is the correct answer.