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| Author: | Bunuel [ 27 Jan 2015, 07:43 ] |
| Post subject: | If x, y, and z are different positive integers, is x prime? |
If x, y, and z are different positive integers, is x prime? (1) xyz = 30 (2) z < x < y Kudos for a correct solution. |
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| Author: | eddyki [ 27 Jan 2015, 08:52 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
Quote: If x, y, and z are different positive integers, is x prime? (1) xyz = 30 (2) z < x < y y=/=x=/=z but all >0 and int. (1) -> x could be 15 (z=1 and y=2) or 3 (z=5 and y=2) , its insuff. (2) -> 100<200<300 (no prime) or 1<2<3 (prime!) -> insuff. (1/2) -> we need 3 distinct factors of 30 -> 1/2/15 or 1/5/6 or 2/3/5 or 1/3/10 . every middle number is a prime, and since z is the smallest pos. int. and y the biggest pos. int., x is a prime number. C |
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| Author: | chetan2u [ 27 Jan 2015, 09:07 ] |
| Post subject: | If x, y, and z are different positive integers, is x prime? |
ans C.. 1) it tells us that x is a divisor of 30..... x,y,z can be 1,2,3,5,6,10,15 2) insufficient..tells us x is middle value combined it tells us that x can be only 2,3,5 or 1,3,10, or 1,2,15 or 1,5,6 or .. so sufficient |
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| Author: | gmat6nplus1 [ 27 Jan 2015, 14:03 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
Bunuel wrote: If x, y, and z are different positive integers, is x prime? (1) xyz = 30 (2) z < x < y Kudos for a correct solution. 1) case_1 xyz=3*2*5 answer=yes; case_2 xyz=1*2*15 answer no. Not sufficient 2) Not sufficient 1+2) x is every time going to be a prime number. Sufficient Answer C. |
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| Author: | DesiGmat [ 28 Jan 2015, 01:33 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
Here we go: x, y, and z are different positive integers St1: xyz = 30 30 = 2*3*5 x = 2, y = 3 and z = 5 (Is X prime? -> true) x = 1, y = 6 and z = 5 (Is X prime? -> false) Not sufficient St2: z < x < y Clearly not sufficient Combining both z = 2, x = 3, y = 5 (Is X prime? -> true) z = 1, x = 2, y = 15 (Is X prime? -> true) z = 1, x = 5, y = 6 (Is X prime? -> true) z = 1, x = 3, y = 10 (Is X prime? -> true) So C is the answer |
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| Author: | santorasantu [ 28 Jan 2015, 07:19 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
Bunuel wrote: If x, y, and z are different positive integers, is x prime? (1) xyz = 30 (2) z < x < y Kudos for a correct solution. Answer c: from stem: x,y and z are positive integers from 1: xyz = 30, prime factors of 30 are 1,2,3 and 5 consider xyz = 2*3*5 = 30 => x is prime, consider xyz = 6*5*1 = 30, x is not prime, 2 answers NSF from 2: z<x<y, considering only this statement, nohing is known, so NSF 1+2: z<x<y, the possible multiples are (note that z, x and y are written accordingly below) 1*2*15 = 30 1*5*6 = 30 1*3*10 = 30 2*3*5 = 30 are the only possible solutions and for all the solutions x is prime, so sufficient. C |
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| Author: | Derkus [ 30 Jan 2015, 23:30 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
Quote: If x, y, and z are different positive integers, is x prime? (1) xyz = 30 (2) z < x < y 1) X*Y*Z = 30 so X*Y*Z must be two factors of 30 * 1 X = 5, Y = 6, Z = 1: Yes X is prime X = 6, Y = 5, Z = 1: No X is not prime 2) Z<X<Y Z = 1 < X = 2 < Y = 3: Yes X is prime Z = 5 < X = 6 < Y = 7: No X is not prime 1+2) All possible pairs of factors of 30 are: (1,30) (2,15) (3,10) (5,6) but you can eliminate (1,30) from our choices because all numbers must be different. Thus ordered triples are: Z = 1 < X = 2 < Y = 15 Z = 1 < X = 3 < Y = 10 Z = 1 < X = 5 < Y = 6 Z = 2 < X = 3 < Y = 5 X = 2, 3, or 5, all of which are Prime. X is Prime, so C. Final Answer: C |
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| Author: | Bunuel [ 02 Feb 2015, 02:49 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
Bunuel wrote: If x, y, and z are different positive integers, is x prime? (1) xyz = 30 (2) z < x < y Kudos for a correct solution. VERITAS PREP OFFICIAL SOLUTION: Solution: C Let’s take statement (2) first: it gives us no values, so it’s INSUFFICIENT. Move on to statement (1). If three different positive integers have a product of 30, those integers must be one of the following sets:{ 1, 3, 10}; {2, 3, 5}; {1, 2, 15}; {1, 5, 6}. X could be prime or not prime; INSUFFICIENT. Combined, consider the four sets of possible integers. The median value is ALWAYS a prime number, so x must be prime. (C). |
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| Author: | pacifist85 [ 07 Feb 2015, 05:20 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
[1] xyz = 30 | NS because: 2*3*5 = 30, x prime 2*1*15 = 30, x prime 15*1*2 = 30, x not prime [2] z<x<y | NS because: 2<3<6, x prime 3<8<10, x not prime [1] and [2], S because: 1<1<30, x prime 1<2<15, x prime 1<3<10, x prime 2<3<5, x prime So, there is no way for x not to be a prime, since, no matter what, y must be the greatest value of the 3 values that multilied together yield 30. Similarly, trying any factor of 30 (it has 8 factors: 1,2,3,5,6,10,15,30) there is no way that the middle one (x) will not be a prime. |
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| Author: | shmba [ 22 Aug 2018, 20:53 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
chetan2u wrote: ans C.. 1) it tells us that x is a divisor of 30..... x,y,z can be 1,2,3,5,6,10,15 2) insufficient..tells us x is middle value combined it tells us that x can be only 2,3,5.. so sufficient 1+2 combined: there should be 4 sets of combinations as stated in other posts. not just 2,3,5. |
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| Author: | bumpbot [ 20 Dec 2022, 08:24 ] |
| Post subject: | Re: If x, y, and z are different positive integers, is x prime? |
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