Question

If x is an integer greater than 1 and y=x+1 divided

by x, which of the following must be true?

I. y does not equal x.
II. y is an integer.
III. xy is greater than x squared

Answer 1

You know, I is true and II is false. III is up to you.

Do you know why?

Answer 2

well

Answer 3

xy will always be greater than x sq. because y is always x+1/x

Answer 4

Well, consider this. Let x be 10.

y = 10 + 1 / 10 = 11/10

xy = 10· 11 / 10 = 11

and x² = 121.

As you can see, III is not true.

Answer 5

wait

Answer 6

I mean x² = 100. Sorry.

Answer 7

the answer booklet says I and III are true

Answer 8

you still there?

Answer 9

That's impossible... Are you sure?

Answer 10

what do you say, son goku?

Answer 11

@micahwood50 y=10+1/10 = 101/10

Answer 12

Or do you actually mean

\[y = x + \frac{1}{x}\]

Answer 13

x+1/x

Answer 14

x and one is not in numerator together, right?

Answer 15

so III is always true

Answer 16

ay y>x
xy>x^2

Answer 17

How come 10+1/10 = 101/10?

Answer 18

*as

Answer 19

you combine digits together?

Answer 20

10+1/10 = (10*10+1)/10 = 101/10

Answer 21

y= x+1/x
so
y>x
xy>x^2

Answer 22

Well, 101 / 10 = 10.1 and x² = 100 so...

Answer 23

yep

Answer 24

good job, guys

Answer 25

Let me show you. \[xy \rightarrow x\left(\frac{x+1}{x}\right) = x + 1\] x + 1 > x²

Or if y = x + (1/x), then:

\[xy \rightarrow x\left( x + \frac{1}{x} \right) = x^2 + 1\]
x² + 1 > x²

In this case, you mean x + (1/x) so yeah, III is true. Sorry for confusion.

Answer 26

good job, guys3

Answer 27

thank you guys for all of the help

Answer 28

these questions are in prep for the PSATs

Answer 29

x + 1 < x² ***

Answer 30

You're welcome. Glad we helped.