Inequalities

15<x-5y<32
0<x-5y-15<17

x between 1-3 and can be a decimal.
y is between 4-5 and can be a decimal and is negative.

the highest value for y = -5(-4.9) = 24.5
the highest value for x = 2.9
2.9+24.5-15 is definitely less than 17.
So (A) should be true.


10<2x-3y<23
0<2x-3y-10<13

the highest value for y = -4.9 and for x = 2.9
2(2.9)-3(-4.9)-10 is again less than 13
So (B) should be true as well.


|X+2Y|<5

x+2y<+-5

x>-5-2y or x<5-2y

again use the highest values.

2.9 > -5+9.8 <<--- false.

for the second one: 2.9<14.8 its true.

however (C) cannot be true because it has 2 answers and one of them doesent work!

Hence the answer should be A & B.

Gurpinder wrote:15<x-5y<32
0<x-5y-15<17

x between 1-3 and can be a decimal.
y is between 4-5 and can be a decimal and is negative.

the highest value for y = -5(-4.9) = 24.5
the highest value for x = 2.9
2.9+24.5-15 is definitely less than 17.
So (A) should be true.


10<2x-3y<23
0<2x-3y-10<13

the highest value for y = -4.9 and for x = 2.9
2(2.9)-3(-4.9)-10 is again less than 13
So (B) should be true as well.


|X+2Y|<5

x+2y<+-5

x>-5-2y or x<5-2y

again use the highest values.

2.9 > -5+9.8 <<--- false.

for the second one: 2.9<14.8 its true.

however (C) cannot be true because it has 2 answers and one of them doesent work!

Hence the answer should be A & B.

Hi,

For 15<x-5y<32 I have the following approach:

-5<Y<-4

=> 25>-5Y>20 = 20<-5Y<25 and 1<X<3 from question:

=> Adding both the above:

21<X-5Y<28

but option (A) 15<x-5y<32 is false..

Can anyone help...

Question:
If 1 < x < 3 and -5 < y < -4, which of the following is/are not true?

1. 15 < x -5y < 32
2. 10 < 2x -3y < 23
3. l x + 2y l < 5

A. Both 1. & 2.
B. Both 2 & 3
C. only 1
D. Only 2
E. Only 3

Solution:
E

Explanation
Using the equations in the stem (1 < x < 3 and -5 < y < -4),
obtain the following equations:

(a)21<x-5y<28
(b)14<2x-3y<21
(c)-9<x+2y<-5

Now, for:
(1)15<X-5Y<32
Using (a), we know that x-5y lies between 21 and 28.
Thus, x-5y definitely lies between 15 and 32. True.

(2)10<2X-3Y<23
Using (b), we know that 2x-3y lies between 14 and 21.
Thus, x-5y definitely lies between 10 and 23. True.

(3)|X+2Y|<5 i.e. -5<x+2y<5
Using (c), we know that x-5y lies between -9 and 5.
However, it's not necessary that x-5y will lie between -5 and 5. False.