Find the LCM of two numbers with prime factorizations x^2*y^3*z . . .

Question

Find the LCM of two numbers, with prime factorization,  x^2 * y^3 * z  and  y*x^9 , where x, y and z are three consecutive prime numbers, in the same order.

(1) xy = z + 1
(2) xz is even

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gurmukh · Answer

LCM= x^9×y^3×z
The product of two prime numbers is always of the form of 6k+1 or 6k-1. 
From statement 1
xy=z+1
If LHS is 6k+1 or 6k-1 then RHS can 6k+2 or 6k, in both cases it not 6k+1 or 6k-1 so no value is possible.
Only possibility is 2,3 and 5. But we don't know the value of x and y. Insufficient
From statement 2
We don't know which one is even.
Insufficient.
Combining
x=2,y=3 and z=5
Sufficient
IMO answer is C

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gurmukh · Answer

LCM= x^9×y^3×z
The product of two prime numbers is always of the form of 6k+1 or 6k-1. 
From statement 1
xy=z+1
If LHS is 6k+1 or 6k-1 then RHS can 6k+2 or 6k, in both cases it not 6k+1 or 6k-1 so no value is possible.
Only possibility is 2,3 and 5. But we don't know the value of x and y. Insufficient
From statement 2
We don't know which one is even.
Insufficient.
Combining
x=2,y=3 and z=5
Sufficient
IMO answer is C

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sauravleo123 · Answer

x.y.z= 3 consec primes in same order
lcm= x^9 y^3 z = ?

Statement 1: xy=z+1

Note that this is only possible when x is even. z will always be odd so z+1 always even

x=2, y=7, z=13
x=2, y=3, z=5
Insufficient
Statement 2: xz=even
x=2, y=7, z=13
x=2, y=3, z=5
Insufficient
Both statements together:
x=2, y=7, z=13
x=2, y=3, z=5
Insufficient 
E

gurmukh · Answer

2,7 and 13 are not consecutive prime numbers

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sauravleo123 · Answer

you are right. Again missed it. C should be correct.

gurmukh · Answer

It really feels bad when you have done a lot of hard work but got the answer wrong because of missing one small point.

sauravleo123 · Answer

Exactly. I always do the difficult parts correctly and always miss the problem because of overlooking the main prompt. Really frustating. I even write down the info, but forget to look at it when doing the problems.

apkhanna · Answer

Since the question does mention that x,y and z are consecutive in the same order, would that automatically make x=2, y=3 and z=5 in the first statement.

And using that same statement from the question, we can assume x=2 in the second statement also.

Thus, I believe the answer should be D

prateek25 · Answer

Shouldn't the answer be d?

x<y<z and x,y,z are consecutive primes.

1. xy= z+1 Only 2, 3, 5 satisfy this and condition above. Sufficient.
2. xy= even, only possible if either x or y =2, so taking condition from question stem (x<y<z), x=2, y=3, z=5. Sufficient

Should be D

adstudy · Answer

LCM of two numbers will be x^9 * y^3 * z^1 where x < y < z and these are consecutive prime numbers; Statement 1: xy = z + 1 Will take a few examples - x = 2, y = 3, z = 5 => Statement 1 is satisfied, x = 3, y = 5, z = 7 => Statement 1 is not satisfied, x = 5, y = 7, z =11 => Statement 1 is not satisfied, x = 7, y = 11, z =13 => Statement 1 is not satisfied, . . . From the pattern we see that, the product of 'xy' is getting much greater than 'z' and will not be able to satisfy Statement 1 equation after the first example. Hence Statement 1 is sufficient as we can now find the exact LCM Statement 2: xz is even The only even prime number is 2 and that is also the smallest of the list of prime numbers. Hence we can deduce that x = 2, making y = 3 and z = 5. Hence Statement 2 is sufficient as we can now find the exact LCM Answer is, hence, D

aka007 · Answer

3*5=15, which is not in the form. You have not considered the even odd aspect of the question. Both statements indl tell us that one of the PM is even, so that makes the lowest PM i.e. x= 2. Therefore, the PMs are 2,3, & 5.

BlueDefender · Answer

I think the question should specify what it means by consecutive primes because 2,3, and 7 are not technically consecutive. 
3, 5, 7 are consecutive
7, 13, 19 are consecutive

bumpbot · Answer

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