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If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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12 Jun 2015, 02:34
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Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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12 Jun 2015, 03:31
Bunuel wrote: If x, y, and z are integers and \(2^x*5^y*z = 6.4*10^6\), what is the value of xy?
(1) z = 20 (2) x = 9
Kudos for a correct solution. CONCEPT: Such Questions always require Prime factorization on both side of the equation to compare the exponent of the same base valuesGiven: \(2^x*5^y*z = 6.4*10^6\) i.e. \(2^x*5^y*z = 64*10^5\) i.e. \(2^x*5^y*z = 2^{11}*5^5\) Question : xy = ?Statement 1: z = 20i.e \(2^x*5^y*20 = 2^{11}*5^5\) i.e \(2^{x+2}*5^{y+1} = 2^{11}*5^5\) i.e. x+2 = 11 and y+1 = 5 i.e. x = 9 and y = 4 Hence, SUFFICIENTStatement 2: x = 9i.e \(2^9*5^y*z = 2^{11}*5^5\) i.e. z must a multiple of \(2^2\) for the exponent of 2 to be equal on both sides of the equation But y still remains unknown Hence, NOT SUFFICIENT
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If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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Updated on: 15 Jun 2015, 07:31
If x, y, and z are integers and \(2^x\)∗\(5^y\)∗z=6.4∗10^6, what is the value of xy?
(1) z = 20
\(2^x\)∗\(5^y\)∗20 = \(2^5\)*\(10^4\)*20 \(2^x\)*\(5^y\) = \(2^9\)*\(5^4\)
x=9,y=4 xy=36 Sufficient
(2) x = 9
\(2^9\)*\(5^y\)*z=\(2^6\)*\(10^5\) \(2^9\)*\(5^y\)*z=\(2^{11}\)*\(5^5\) if y=5 then z=4 if y=4 then z=20 if y=3 then z=100
So y can take any value ranging from 0 to 5.
Insufficient
Ans : A
Originally posted by ManojReddy on 12 Jun 2015, 03:54.
Last edited by ManojReddy on 15 Jun 2015, 07:31, edited 1 time in total.



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Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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15 Jun 2015, 04:42
Bunuel wrote: If x, y, and z are integers and \(2^x*5^y*z = 6.4*10^6\), what is the value of xy?
(1) z = 20 (2) x = 9
Kudos for a correct solution. MANHATTAN GMAT OFFICIAL SOLUTION:Express both sides of the equation in terms of prime numbers. \(2^x*5^y*z = 6.4*10^6=2^{11}*5^5\). The right side of the equation is composed of only 2's and 5's. The left side of the equation has x number of 2's and y number of 5's along with some factor z. This unknown factor z must be composed of only 2's and/or 5's, or it must be 1 (i.e. with no prime factors). If z = 1, then x = 11 and y = 5. If z = 2^?*5^?, where the exponents are not 0, then x and y will depend on the value of those exponents. The rephrased question is thus “How many factors of 2 and 5 are in z?” (1) SUFFICIENT: If \(z = 20 = 2^2*5^1\), then we have the answer to our rephrased question. Incidentally,this implies that \(2^x*5^y(2^2*5^1) = 2^{11}*5^5\), so x = 9 and y = 4, making xy = 36. (2) INSUFFICIENT: If x = 9, then \(2^x*5^y*z = 2^{11}*5^5\) \(2^9*5^y*z = 2^{11}*5^5\) \(z=2^2*5^{5y}\) While this tells us the number of 2's among z's factors, we still do not know how many factors of 5 are in z. The correct answer is A.
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If x,y and z are integers and 2^x 5^y z = 6.4*10^6 , what is the value
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22 Apr 2018, 06:10
If x,y and z are integers and \(2^x 5^y z = 6.4*10^6\) , what is the value of xy?
1.z=20 2.x=9



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If x,y and z are integers and 2^x 5^y z = 6.4*10^6 , what is the value
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22 Apr 2018, 06:28
selim wrote: If x,y and z are integers and \(2^x 5^y z = 6.4*10^6\) , what is the value of xy?
1.z=20 2.x=9 \(2^x 5^y z = 6.4*10^6=>64*10^5\) \(2^x 5^y z = 2^{10}5^5\). Hence to know the value of \(xy\), we need to know the value of \(z\) Statement 1: provides the value of \(z\). SufficientFor the sake of calculation, \(2^x 5^y*20 = 2^{10}5^5=>2^{x+2}*5^{y+1}=2^{10}5^5\) \(=>x+2=10=>x=8\) \(=>y+1=5=>y=4\). Hence \(xy=8*4=32\) Statement 2: nothing can be said about the value of y & z. InsufficientOption A



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Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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22 Apr 2018, 20:47



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Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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08 May 2018, 23:01
I) 2^x*5^y=32*10^4 So y=4 and x=9 To make up equality of eqn so sufficient II) we know x but we don't know z Z=1 or z=5 or 10 Can result in different values of xy So insufficient A is answer Posted from my mobile device
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Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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24 Jun 2018, 05:12
Bunuel wrote: If x, y, and z are integers and \(2^x*5^y*z = 6.4*10^6\), what is the value of xy?
(1) z = 20 (2) x = 9
Target question: What is the value of xy? Given: x, y, and z are integers and (2^x)(5^y)(z) = (6.4)(10^6) Since the left side of the given equation has been factored by primes, let's find the prime factorization of (6.4)(10^6) (6.4)(10^6) = (6.4)(10^1)(10^5) = (64)(10^5) = (2^6)(10^5) = (2^6)(2^5)(5^5) = (2^11)(5^5) So, we have: (2^x)(5^y)(z) = (2^11)(5^5) Statement 1: z = 20 Take (2^x)(5^y)(z) = (2^11)(5^5) and replace z with 20... We get: (2^x)(5^y)(20) = (2^11)(5^5) Rewrite 20 as follows: (2^x)(5^y)(2^2)(5) = (2^11)(5^5) Divide both sides of the equation by 2^2 to get: (2^x)(5^y)(5) = (2^9)(5^5) Divide both sides of the equation by 5 to get: (2^x)(5^y) = (2^9)(5^4) At this point, we can see that x = 9 and y = 4, so xy = (9)(4) = 36So, the answer to the target question is xy = 36Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: x = 9Take (2^x)(5^y)(z) = (2^11)(5^5) and replace x with 9... We get: (2^9)(5^y)(z) = (2^11)(5^5) Divide both sides of the equation by 2^9 to get: (5^y)(z) = (2^2)(5^5)From here, we can see that there are several values of x and z that satisfy the equation (5^y)(z) = (2^2)(5^5) . Here are two possible cases: Case a: y = 5 and z = 2^2. We already know that x = 9, so the answer to the target question is xy = (9)(5) = 45Case b: y = 4 and z = (2^2)(5). We already know that x = 9, so the answer to the target question is xy = (9)(4) = 36Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A Cheers, Brent
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Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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26 Jun 2018, 17:11
Bunuel wrote: If x, y, and z are integers and \(2^x*5^y*z = 6.4*10^6\), what is the value of xy?
(1) z = 20 (2) x = 9 Notice that 6.4 * 10^6= 64 * 10^5 = 2^6 * 2^5 * 5^5 = 2^11 * 5^5 Statement One Alone: z = 20 Thus we have: 2^x + 5^y * 20 = 2^11 * 5^5 2^x + 5^y * 2^2 * 5 = 2^11 * 5^5 2^(x+2) + 5^(y+1) = 2^11 * 5^5 Since x and y are integers, x + 2 = 11 and y + 1 = 5. So x = 9 and y = 4 and xy = 9(4) = 36. Statement one alone is sufficient. Statement Two Alone: x = 9 Thus we have: 2^9 * 5^y * z = 2^11 * 5^5 5^y * z = 2^2 * 5^5 However, we can’t determine a unique value for y. For example, if z = 4, then y = 5. On the other hand, if z = 20, then y = 4. Statement two alone is not sufficient. Answer: A
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Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu
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27 Jun 2018, 04:14
math revolution how to apply variable approach here..??




Re: If x, y, and z are integers and 2^x*5^y*z = 6.4*10^6, what is the valu &nbs
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27 Jun 2018, 04:14






