If 1

Question

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)

VeritasPrepBrian · Accepted Answer

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.

pushpitkc · Answer

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.

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=qo1Y42BepxA

ScottTargetTestPrep · Answer

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

Answer: E

FANewJersey · Answer

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

septwibowo · Answer

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

brains · Answer

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

BijayKru · Answer

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.

gmexamtaker1 · Answer

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.

OjhaShishir · Answer

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.

GMATinsight · Answer

Answer: Option E

Video solution by  GMATinsight

https://www.youtube.com/watch?v=YTf2L54hoIE

Asitima · Answer

Knowing all are positive integers, following should be true even if we include fractions/decimals? Given, 1x+1>y+1 Hence a product of z and (x+y) will produce the highest number. Option E

nilsruge · Answer

a * b, where a + b is constant, is maximized if a = b, so in this case we try to find factors that are as close to each other as possible.

As x < y < z, we know that (x+y) * z is the highest product we can get.

Aboyhasnoname · Answer

At the first go, we should eliminate A and B because the rest will definitely give us bigger numbers than A and B..Since the inside of the bracket is greater in all cases {x, y, z being greater than 1}... 
Now.... Let's Just Open them ..C. xy and xz and D. xy and yz...therefore..D is bigger...since since xy is common in both and yz is greater... 
Now D and E..E is xz and yz....Now here ..Yz is common in both but xz us greater than x and y ..Hence E is the greater...

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

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GMAT Problem Solving (PS) Questions

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

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