If |10y - 4| > 7 and y < 1, which of the following could be y?
A) -0.8
B) -0.1
C) 0.1
D) 0
E) 1
Option E) y = 1 can be eliminated because y < 1 is the condition it should satisfy.
Option D) y = 0 and C) y = 0. 1 can be eliminated because -7<10y - 4<7 in both the cases
Option B) y = -0.1, 10y - 4 = -1-4 = -5. Implies |10y - 4| = 5 < 7 no the answer
Option A) y = -0.8, Is Correct ! Oh ok let me check.|10y - 4| = |-8-4| = 12 > 7 Superb!
Absolute Vlaue Question
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neelgandham
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GmatMathPro
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What did you do to get B?Strongt wrote:If |10y - 4| > 7 and y < 1, which of the following could be y?
A) -0.8
B) -0.1
C) 0.1
D) 0
E) 1
Could someone explain why the answer is A and not B
Plugging in values works well here, as neelgandham demonstrates. If you want an algebraic way to solve it, you can do the following:
If, |10y-4|>7 then either 10y-4>7 or 10y-4<-7 (do you see why?) Now, solve these two inequalities one at a time:
10y-4>7
10y>11
y>1.1
OR
10y-4<-7
10y<-3
y<-0.3
So the solution is y<-0.3 OR y>1.1; But the questions specifies that y<1, so we can ignore the second part. y=-0.8 is the only one that satisfies both statements. Hence, ans: A
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Strongt
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I guess that's what I'm missingGmatMathPro wrote:What did you do to get B?Strongt wrote:If |10y - 4| > 7 and y < 1, which of the following could be y?
A) -0.8
B) -0.1
C) 0.1
D) 0
E) 1
Could someone explain why the answer is A and not B
Plugging in values works well here, as neelgandham demonstrates. If you want an algebraic way to solve it, you can do the following:
If, |10y-4|>7 then either 10y-4>7 or 10y-4<-7 (do you see why?) Now, solve these two inequalities one at a time:
10y-4>7
10y>11
y>1.1
OR
10y-4<-7
10y<-3
y<-0.3
So the solution is y<-0.3 OR y>1.1; But the questions specifies that y<1, so we can ignore the second part. y=-0.8 is the only one that satisfies both statements. Hence, ans: A
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GmatMathPro
- GMAT Instructor
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To simplify matters, let's look at what it would mean for |x|>7. This says that the absolute value of x is greater than 7. But what does this mean? Essentially it means that the size of x, regardless of the sign, is bigger than 7. Clearly numbers bigger than 7 satisfy this. But numbers less than -7 also satisfy it. For example, |-8|=8, which is bigger than 7. The following number line shows all of the numbers that satisfy this inequality:
.
As you can see, this includes all numbers such that x>7 OR x<-7. So if we encounter |x|>7, we can always rewrite it equivalently as x>7 OR x<-7.
When we get to a more complicated expression, such as |4y-10|>7, it will work the exact same way. We can break it down into two separate inequalities by thinking, "for this to be true, the expression inside will either have to be greater than 7, OR less than -7, which, mathematically is written as 4y-10>7 OR 4y-10<-7. Now that we've rewritten it without the absolute value bars, we can use a traditional algebraic approach to solve for the solution set.
. As you can see, this includes all numbers such that x>7 OR x<-7. So if we encounter |x|>7, we can always rewrite it equivalently as x>7 OR x<-7.
When we get to a more complicated expression, such as |4y-10|>7, it will work the exact same way. We can break it down into two separate inequalities by thinking, "for this to be true, the expression inside will either have to be greater than 7, OR less than -7, which, mathematically is written as 4y-10>7 OR 4y-10<-7. Now that we've rewritten it without the absolute value bars, we can use a traditional algebraic approach to solve for the solution set.
Strongt wrote:I guess that's what I'm missingGmatMathPro wrote:What did you do to get B?Strongt wrote:If |10y - 4| > 7 and y < 1, which of the following could be y?
A) -0.8
B) -0.1
C) 0.1
D) 0
E) 1
Could someone explain why the answer is A and not B
Plugging in values works well here, as neelgandham demonstrates. If you want an algebraic way to solve it, you can do the following:
If, |10y-4|>7 then either 10y-4>7 or 10y-4<-7 (do you see why?) Now, solve these two inequalities one at a time:
10y-4>7
10y>11
y>1.1
OR
10y-4<-7
10y<-3
y<-0.3
So the solution is y<-0.3 OR y>1.1; But the questions specifies that y<1, so we can ignore the second part. y=-0.8 is the only one that satisfies both statements. Hence, ans: A
