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555-605 (Medium)|   Algebra|      
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Bunuel
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What is the value of x ? (1) 6x - 9y = 24 (2) 1.5y = x - 4 15 Feb 2023, 04:51
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E
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25% (medium)

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71% (01:00) correct 29% (00:53) wrong based on 100 sessions

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What is the value of x ?

(1) 6x - 9y = 24
(2) 1.5y = x - 4
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E
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What is the value of x ? (1) 6x - 9y = 24 (2) 1.5y = x - 4 15 Feb 2023, 08:25
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What is the value of x ?

(1) 6x - 9y = 24
(2) 1.5y = x - 4

Multiplying equation (2) by 6, will result in equation (1), Hence equation (1) & (2) both are same.
So, 'x' has infinite number of values.

6*(1.5y) = 6*(x - 4)
9y = 6x - 24
6x - 9y = 24 equation (1) = equation (2)
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What is the value of x ? (1) 6x - 9y = 24 (2) 1.5y = x - 4 Updated on: 31 Mar 2023, 02:07
Originally posted by Afn24 on 28 Mar 2023, 01:02.
Last edited by Afn24 on 31 Mar 2023, 02:07, edited 1 time in total.
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But will it be the same in this question aswell because of the presence of a negative sign? And I don't understand how the answer is E, according to me it should be (D)


Appreciate the help. Thanks in advance.
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What is the value of x ? (1) 6x - 9y = 24 (2) 1.5y = x - 4 28 Mar 2023, 08:12
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Bunuel
What is the value of x ?
(1) 6x - 9y = 24
(2) 1.5y = x - 4
Show more
Solution:
Pre Analysis:
  • We are asked the value of x

Statement 1: 6x - 9y = 24
  • Given equation \(6x-9y=24\) or \(2x-3y=8\) (dividing by 3) is only one equation with 2 variables (with no constraint)
  • Thus, statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2: 1.5y = x - 4
  • Given equation \(1.5y = x - 4\) or \(x-1.5y=4\) or \(2x-3y=8\) (multiplying by 2) is only one equation with 2 variables (with no constraint)
  • Thus, statement 2 alone is also not sufficient

Combining:
  • Both the statements are the same equation in different forms and different co-efficient


Hence the right answer is Option E
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What is the value of x ? (1) 6x - 9y = 24 (2) 1.5y = x - 4 28 Mar 2023, 14:09
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Afn24
Dear Sir avigutman, I learned from one of your videos to use a method of coinciding LCM for Questions such as above.
Ex. 5x + 7y = 37, In this equation X and Y will coincide only once before 37, i.e. at 35 so x and y will have a unique value.

But will it be the same in this question aswell
Show more
No, Afn24. That method only works when there’s an integer constraint. Here, x and y aren’t necessarily integers. I suggest that you review *why* the method works, so that you’re less likely to misuse it.

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What is the value of x ? (1) 6x - 9y = 24 (2) 1.5y = x - 4 17 Jun 2024, 06:59
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