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Director  B
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If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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Question Stats: 90% (01:01) correct 10% (01:06) wrong based on 1377 sessions

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If 1 < x < y < z, which of the following has the greatest value?

A. z(x + 1)
B. z(y + 1)
C. x(y + z)
D. y(x + z)
E. z(x + y)
Veritas Prep Representative G
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Re: If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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septwibowo wrote:
I'm curious. Do we have other ways to solve this problem WITHOUT plug in the number?

Yeah really good question. If you distribute the multiplication you can get really direct comparisons between the quantities:

(A) zx + z

(B) zy + z

(C) xy + xz

(D) yx + yz

(E) zx + zy

(A) and (B) should be easy to eliminate since in each case you can see that choice (E) includes one of the two terms (zx or zy) but then adds something bigger than z to it.

Then for (C) vs. (D), note that each includes xy, but then (D) adds a bigger second term (since y > x, then yz > xz). So (D) is bigger than (C). And when you compare (E) to (D), you can use the same logic: each includes a yz term, but then (E) adds something bigger to it (zx > yx since z > y). So now you have algebraic proof that (E) is greater than all the other four.
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Senior PS Moderator V
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If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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Plug values x=2,y=3,z=4 , which satisfies the condition 1<x<y<z

If we use this values in the answer options
A. z(x + 1) = 4(3) = 12
B. z(y + 1) = 4(4) = 16
C. x(y + z) = 2(7) = 14
D. y(x + z) = 3(6) = 18
E. z(x + y) = 4(5) = 20

Therefore, z(x+y) - Option E has the greatest value.
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Target Test Prep Representative V
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Re: If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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AbdurRakib wrote:
If 1 < x < y < z, which of the following has the greatest value?

A. z(x + 1)
B. z(y + 1)
C. x(y + z)
D. y(x + z)
E. z(x + y)

We can let x = 2, y = 3, and z = 4, and we have:

A) z(x+1)

4(3) = 12

B) z(y+1)

4(4) = 16

C) x(y+z)

2(7) = 14

D) y(x+z)

3(6) = 18

E) z(x+y)

4(5) = 20

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Intern  B
Joined: 01 May 2017
Posts: 33
Re: If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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whenever we see that there are variables in all answer choices and variables in the question (without clear values) then we can pick easy number(s), and apply the numbers across all the options and see which option gives the required result. In this case, as the above posters have pointed out, we can pick numbers as x=2, y=3, and z=4 and apply then to all the options, finding that option (E) gives the largest result. So E is the answer
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Re: If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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I'm curious. Do we have other ways to solve this problem WITHOUT plug in the number?
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Re: If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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Since 1<x<y<z , so x,y,z are all positive real numbers
Now assume x= 1+m
since y>x , so y can be assumed as y= x+ n
and z = y + o.
Putting in the corresponding values of x & y in z, we have
Now z= 1+m+n+o

Since all are positive numbers
so the greatest value can only be achieved by multiplying the greatest number by the sum of other two( This approach is subjective to the Options given in answers because answer is expressed as only the product of one number with the sum of the other two). So mathematically it can be concluded that z has to be individual number and the other should be x+y.

Note: We can also conclude the answer by substituting the value of z , y, x in answer choices.

Hope I am right
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Manager  B
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Location: India
Re: If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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x=2,y=3,z=4 , which satisfies the condition 1<x<y<z

If we use this values in the answer options
A. z(x + 1) = 4(3) = 12
B. z(y + 1) = 4(4) = 16
C. x(y + z) = 2(7) = 14
D. y(x + z) = 3(6) = 18
E. z(x + y) = 4(5) = 20 So max value we are getting is E.
Manager  B
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Re: If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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Hello guys,
A prompt question , in problems such as this one , if we pick numbers (e.g integers) should we also check with decimals or an another set of numbers just to be sure, or is it just a waste of time? If we got two correct answers its obvious that we should test other numbers but Im refering specifically on this type of problems , in which easily by picking 2-3-4 we came up with an exact answer.
Intern  B
Joined: 19 Dec 2019
Posts: 19
Re: If 1 < x < y < z, which of the following has the greatest value?  [#permalink]

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Because the question is asking: which of the following has the greatest value?

So, if we pick "any numbers" (in accordance with 1 < x < y < z), the answer will be consistent.

So, I believe we don't need to pick various "combinations" of x, y and z. So, we don't need to check with decimals. Re: If 1 < x < y < z, which of the following has the greatest value?   [#permalink] 21 Jan 2020, 05:55
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