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Joined: 19 Oct 2018
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A is a three digit number such that z is the units digit, y is the ten
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01 Sep 2019, 17:07
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39% (03:10) correct 61% (03:18) wrong based on 28 sessions
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M is a three digit number such that z is the units digit, y is the tens digit and x is the hundreds digit of M. Also, M= y*(10z+y), where y and 10z+y are prime numbers. Find x+y+z ? A. 12 B. 14 C. 17 D. 18 E. 22 Kudos for a correct solution.
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Re: A is a three digit number such that z is the units digit, y is the ten
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01 Sep 2019, 18:57
3 digit number xyz can be written as xyz=100x+10y+z ,given y is prime so the max value of y is 7 ,now plug in values for z which ranges from 1to 9 considering y= 7 ,for z start from the bottom,I am substituting 9, now z= 10*9+7=97,given m=y*(10z+y)= 7 *97= 679 , Sox+y+z= 6+7+9= 22, the answer is E
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Re: A is a three digit number such that z is the units digit, y is the ten
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04 Sep 2019, 01:53
y is a prime, so possible values of y: 2,3,5,7,9 but (10z+y) is also a prime number number; so possible values of y: 3,7,9 (22,25,32,35 etc can never be prime). Starting from maximum 2 digit prime number (we can start from min i.e. 13 as well, but we know 13*3 will never be a 3 digit number. we will have to check a lot of values to find first 3 digit number, so we start from back) => 10z+y = 97; 97*7=679 => 6+7+9 = 22
Thus E



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Re: A is a three digit number such that z is the units digit, y is the ten
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04 Sep 2019, 02:16
You are very close to the perfect solution. Though you get the correct answer, there are couple of mistakes in your solution. 1. 9 is not a prime number. 2. We don't have to look for a lot of values. As y is a prime number, y can be 2,3,5 or 7 When y=2 or 5, 10z+y can never be prime. Hence y can be 3 or 7 M=100x+10y+z=y*(10z+y) \(100x+10y+z=10yz+y^2\) Hence unit digit of \(y^2\) is equal to z z=unit digit of \(3^2\) or \(7^2\) z=9 in both cases 1. when y=3, 10z+y=93, which is not a prime 2. when y=7, 10z+y=97, which is a prime M= 7*97=679 jimar wrote: y is a prime, so possible values of y: 2,3,5,7,9 but (10z+y) is also a prime number number; so possible values of y: 3,7,9 (22,25,32,35 etc can never be prime). Starting from maximum 2 digit prime number (we can start from min i.e. 13 as well, but we know 13*3 will never be a 3 digit number. we will have to check a lot of values to find first 3 digit number, so we start from back) => 10z+y = 97; 97*7=679 => 6+7+9 = 22
Thus E



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Re: A is a three digit number such that z is the units digit, y is the ten
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01 Dec 2019, 09:23
nick1816 wrote: M is a three digit number such that z is the units digit, y is the tens digit and x is the hundreds digit of M. Also, M= y*(10z+y), where y and 10z+y are prime numbers. Find x+y+z ? A. 12 B. 14 C. 17 D. 18 E. 22 Kudos for a correct solution. Why can't z be 4? then We can have 7*47 = 329 = 3+2+9 = 14. What is wrong with this solution?



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Re: A is a three digit number such that z is the units digit, y is the ten
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01 Dec 2019, 09:48
If M is 329, value of z is 9. You're getting different values of z, making your solution incorrect. Krish728 wrote: nick1816 wrote: M is a three digit number such that z is the units digit, y is the tens digit and x is the hundreds digit of M. Also, M= y*(10z+y), where y and 10z+y are prime numbers. Find x+y+z ? A. 12 B. 14 C. 17 D. 18 E. 22 Kudos for a correct solution. Why can't z be 4? then We can have 7*47 = 329 = 3+2+9 = 14. What is wrong with this solution?



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Re: A is a three digit number such that z is the units digit, y is the ten
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01 Dec 2019, 10:28
nick1816 wrote: If M is 329, value of z is 9. You're getting different values of z, making your solution incorrect. Krish728 wrote: nick1816 wrote: M is a three digit number such that z is the units digit, y is the tens digit and x is the hundreds digit of M. Also, M= y*(10z+y), where y and 10z+y are prime numbers. Find x+y+z ? A. 12 B. 14 C. 17 D. 18 E. 22 Kudos for a correct solution. Why can't z be 4? then We can have 7*47 = 329 = 3+2+9 = 14. What is wrong with this solution? I didn't understand. Can you please explain?



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Re: A is a three digit number such that z is the units digit, y is the ten
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01 Dec 2019, 11:23
Krish728 Bro you are considering value of z=4 So value of M must be 'xy4', as M='xyz' But, you are getting value of M= 329(value of z is 9); hence, you are contradicting your initial consideration




Re: A is a three digit number such that z is the units digit, y is the ten
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01 Dec 2019, 11:23






