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contactakanksha
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If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true? Updated on: 03 Mar 2020, 06:24
Originally posted by contactakanksha on 03 Mar 2020, 05:22.
Last edited by Bunuel on 03 Mar 2020, 06:24, edited 2 times in total.
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

54% (02:31) correct 46% (02:32) wrong based on 336 sessions

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

i. 15 < x - 5y < 32
ii. 10 < 2x - 3y < 23
iii. |x + 2y| < 5

(A) Only i.
(B) Only ii.
(C) Only iii.
(D) Both i. and ii.
(E) Both ii. and iii.
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Official Answer
C
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If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true? Updated on: 03 Mar 2020, 06:27
Originally posted by shameekv1989 on 03 Mar 2020, 05:34.
Last edited by shameekv1989 on 03 Mar 2020, 06:27, edited 1 time in total.
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contactakanksha
If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true?

i. 15 < x - 5y < 32
ii. 10 < 2x - 3y < 23
iii. |x + 2y| < 5

(A) Only i.
(B) Only ii.
(C) Only iii.
(D) Both i. and ii.
(E) Both ii. and iii.
Show more

contactakanksha - Can you add the OA to the question.

Solution =>

i) -5 < y < -4 =>
20 < -5y < 25 (Multiplying by -5 changes sign)
1 < x < 3

Adding we get 21 < x-5y < 28 --- It covers all the values from the inequality

ii) -5 < y < -4 =>
12 < -3y < 15 (Multiplying by -3 changes sign)
1 < x < 3 =>
2 < 2x < 6

Adding we get 14 < 2x-3y < 21 ---- It covers all the values from the inequality

iii) 1 < x < 3 and -5 < y < -4

-5 < y < -4 => -10 < 2y < -8

-9 < x+2y < -5

5 < |x+2y| < 9 --- It does not satisfy the inequality

i) and ii) must always be true iii) will not be true then

Answer - C
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If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true? 03 Mar 2020, 06:13
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shameekv1989
contactakanksha
If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true?

i. 15 < x - 5y < 32
ii. 10 < 2x - 3y < 23
iii. |x + 2y| < 5

(A) Only i.
(B) Only ii.
(C) Only iii.
(D) Both i. and ii.
(E) Both ii. and iii.

contactakanksha - Can you add the OA to the question.

Solution =>

i) -5 < y < -4 =>
20 < -5y < 25 (Multiplying by -5 changes sign)
1 < x < 3

Adding we get 21 < x-5y < 28 --- It covers all the values from the inequality

ii) -5 < y < -4 =>
12 < -3y < 15 (Multiplying by -3 changes sign)
1 < x < 3 =>
2 < 2x < 6

Adding we get 14 < 2x-3y < 21 ---- It covers all the vlaues from the inequality

iii) 1 < x < 3 and -5 < y < -4

-5 < y < -4 => -10 < 2y < -8

-9 < x+2y < -5

5 < |x+2y| < 9 --- It does not satisfy the inequality

i) and ii) must always be true

I am getting D as the answer.
Show more

Hi Bunuel , could you please verify the solution?
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If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true? 03 Mar 2020, 06:25
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contactakanksha
shameekv1989
contactakanksha
If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true?

i. 15 < x - 5y < 32
ii. 10 < 2x - 3y < 23
iii. |x + 2y| < 5

(A) Only i.
(B) Only ii.
(C) Only iii.
(D) Both i. and ii.
(E) Both ii. and iii.

contactakanksha - Can you add the OA to the question.

Solution =>

i) -5 < y < -4 =>
20 < -5y < 25 (Multiplying by -5 changes sign)
1 < x < 3

Adding we get 21 < x-5y < 28 --- It covers all the values from the inequality

ii) -5 < y < -4 =>
12 < -3y < 15 (Multiplying by -3 changes sign)
1 < x < 3 =>
2 < 2x < 6

Adding we get 14 < 2x-3y < 21 ---- It covers all the vlaues from the inequality

iii) 1 < x < 3 and -5 < y < -4

-5 < y < -4 => -10 < 2y < -8

-9 < x+2y < -5

5 < |x+2y| < 9 --- It does not satisfy the inequality

i) and ii) must always be true

I am getting D as the answer.

Hi Bunuel , could you please verify the solution?
Show more

Check the highlighted part: ...which of the following is/are NOT true?
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If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true? 03 Mar 2020, 07:50
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If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true?

i. 15 < x - 5y < 32
ii. 10 < 2x - 3y < 23
iii. |x + 2y| < 5

(A) Only i.
(B) Only ii.
(C) Only iii. --> correct
(D) Both i. and ii.
(E) Both ii. and iii.

Solution:
(i)15 < x - 5y < 32 --(a)
1 < x < 3 --(p)
-5 < y < -4
=> -25<5y<-20
=> 20<-5y<25 ---(q)
(p)+(q)=>
21<x-5y<28 ---(r)
(r) is covered by (a) => so (i) is true

(ii)10 < 2x - 3y < 23 --(b)
1 < x < 3 --(p)
=> 2 < 2x < 6--(s)
-5 < y < -4
=> -15<3y<-12
=> 12<-3y<15 ---(t)
(s)+(t)=>
14<2x-3y<21 ---(u)
(u) is covered by (b) => so (ii) is true

(iii)|x + 2y| < 5
=> -5 < x+2y < +5 --(c)
1 < x < 3 --(p)

-5 < y < -4
=> -10<2y<-8 --(v)
(p)+(v)=>
-9<x+2y<-5 ---(w)
(w) is NOT covered by (c) => so (iii) is NOT true
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If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true? 22 Jun 2024, 07:50
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­↧↧↧ Detailed Video Solution to the Problem ↧↧↧


Given that 1 < x < 3 ...(1)
and -5 < y < -4 ...(2)

Lets start checking each option

i. 15 < x - 5y < 32

-5 < y < -4

Multiplying with -1 on all the sides we get
5 > -y > 4 (note that sign of the inequality reverses as we multiplied with -1)
=> 4 < -y < 5 ...(3)

(1) + 5*(3)
1 + 5*4 < x - 5*y < 3 + 5*5
=> 21 < x - 5y < 28
=> 15 < x-5y < 32 is TRUE

ii. 10 < 2x - 3y < 23

2*(1) + 3*(3)
2*1 + 3*4 < 2*x - 3*y < 2*3 + 3*5
=> 14 < 2x - 3y <21
=> 10 < 2x - 3y < 23 is TRUE

iii. |x + 2y| < 5

=> -5 < x +2y < 5 [ Watch this video to MASTER Absolute Value ]

(1) + 2*(2)
1 + 2*(-5) < x + 2*y < 3 + 2*(-4)
=> -9 < x + 2y < -5
=> -5 < x +2y < 5 is FALSE

So, Answer will be C
Hope it helps!

Watch the following video to MASTER Inequalities

­
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If 1 < x < 3 and -5 < y < -4, which of the following is/are NOT true? 02 Oct 2025, 10:16
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