Question

If the difference of two numbers is less than the

sum of the numbers, which of the following must

be true?

Answer 1

Ok, what are the choices?

Answer 2

A. Neither number is positive

Answer 3

B. At least one of the numbers is positive

Answer 4

C. Exactly one of the numbers is positive

Answer 5

D. Both numbers are positive

Answer 6

E. None of these statements must be ture

Answer 7

true

Answer 8

those are my choices

Answer 9

so

Answer 10

D.

Answer 11

(x-y)<(x+y)

Answer 12

Nope

Answer 13

Answer booklet says B.

Answer 14

At least one of the numbers is positive

Answer 15

so

Answer 16

2+2 and 2-2?

Answer 17

ehh?

Answer 18

so they are saying the difference is 4 and the sum is 0?

Answer 19

wah

Answer 20

anything, guys?

Answer 21

you guys still there?

Answer 22

ehh

Answer 23

how about like this...,
let x,y be the numbers, such that x>y,so

x-y < x+y
-y<y
2y>0
y>0

I assume that x>y, then x>0,

I'm not sure about this..,

Answer 24

x is greater than 0

Answer 25

x is greater than y...

Answer 26

then, should not both the numbers be positive?

Answer 27

Yes, the answer is B

Answer 28

how?

Answer 29

Only one number needs to be positive.

Answer 30

chihi said both the numbers are positive

Answer 31

how?

Answer 32

y is greater than 0

Answer 33

x is greater than y

Answer 34

so they should both be positive

Answer 35

The first # can be negative. Then, if you subtract a positive #, that answer is smaller than if you were to add a positive #.

Answer 36

hold up

Answer 37

So, the answer is B.

Answer 38

-2-2=-4

Answer 39

-2+2=0

Answer 40

ahh

Answer 41

so not

Answer 42

2+2=4?

Answer 43

2-2=0?

Answer 44

And 0 is greater than -4, so the answer is B.

Answer 45

when we talk about the difference, isn't it the absolute value?
so the difference between x and y, it's |x-y|, that's why I assume x>y,
how?

Answer 46

k

Answer 47

so

Answer 48

ehh

Answer 49

(x+y)<(x-y)

Answer 50

x+y<x-y

Answer 51

2y<0

Answer 52

y<0

Answer 53

x+0<x-0

Answer 54

I got confuse
let's ask others
@sauravshakya
@hartnn

Answer 55

so y<0

Answer 56

It's actually a poorly-worded problem, because if one interprets the question for EVERY set of x and y (that is, if you allow x and y to be switched around), THEN they have to be both positive.

Answer 57

yeah

Answer 58

x-y<x+y

Answer 59

and this is a PSAT QUESTION!

Answer 60

so

Answer 61

x equals 0

Answer 62

But IF (and this is the way they mean the problem to be) they allow the x and y to picked so that the first # is negative, THEN only one number needs to be positive. It's a very VERY poorly worded question.

Answer 63

which is neither positive or negative?

Answer 64

so

Answer 65

y<0

Answer 66

so lets say

Answer 67

x+1<x-1

Answer 68

x<x-2

Answer 69

0<2?

Answer 70

0<-2?

Answer 71

so, I understand y<0

Answer 72

but how do we solve for x?

Answer 73

luisz, it would be helpful if you did not break up your posts into so many little posts. It is quite impossible to follow your train of thought when you do that.

Answer 74

x cancels to be 0 in the problem

Answer 75

sorry

Answer 76

I'll let you guys talk now

Answer 77

if we talk about the difference, I think it doesn't matter which number at first,
the difference between -1 and 2 is 3.., no matter which number at the front.., right?

Answer 78

I already gave my answer. Just read it.

Answer 79

The first # can be negative. Then, if you subtract a positive #, that answer is smaller than if you were to add a positive #.

Answer 80

-2-1=-3

Answer 81

-2+1=-1

Answer 82

difference is smaller

Answer 83

As I said earlier also,
I think Both numbers must be positive.

Answer 84

but only one number needs to be positive

Answer 85

like tcarrol said, this a poorly worded problem

Answer 86

But why would they poorly word a PSAT QUESTION?

Answer 87

The first # can be negative. Then, if you subtract a positive #, that answer is smaller than if you were to add a positive #. It's actually a poorly-worded problem, because if one interprets the question for EVERY set of x and y (that is, if you allow x and y to be switched around), THEN they have to be both positive. But IF (and this is the way they mean the problem to be) they allow the x and y to picked so that the first # is negative, THEN only one number needs to be positive. It's a very VERY poorly worded question.

Answer 88

(x-y)<x+y
2y>0
y>0
so y must be positive.
now for x,
let x be positive, ex
4-2<4+2<----correct!
let x be negative.
-4-4<-4+2<-----correct!
so x can be + or -
so
B. atleast.

Answer 89

-4-2<-4+2<-----correct!

Answer 90

ahh

Answer 91

must is the key word...

Answer 92

but x could be positive

Answer 93

whatever

Answer 94

lets end this discussion

Answer 95

I am going to make lunch now

Answer 96

see you guys end a bit

Answer 97

yup, x could be + or - any, so atleast 1 should be +.

Answer 98

see ya :)