Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

\(y=|x+3|+|4-x|\) two check points: \(x=-3\) and \(x=4\) (check point: the value of \(x\) when expression in || equals to zero), hence three ranges to consider:

A. \(x<{-3}\) --> \(y=| x + 3| +|4-x| =-x-3+4-x=-2x+1\), which means that when \(x\) is in the range {-infinity,-3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range);

B. \(-3\leq{x}\leq{4}\) --> \(y=|x+3|+|4-x|=x+3+4-x=7\), which means that when \(x\) is in the range {-3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range);

C. \(x>{4}\) --> \(y=|x+3|+|4-x|=x+3-4+x=2x-1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range).

Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {-3,4}

(1) \(x<4\) --> not sufficient (\(x<4\) but we don't know if it's \(\geq{-3}\)); (2) \(x>-3\) --> not sufficient (\(x>-3\) but we don't know if it's \(\leq{4}\));

(1)+(2) \(-3<x<4\) exactly the range we needed, so \(y=7\). Sufficient.

Answer: C.

OR: looking at \(y=|x+3|+|4-x|\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4-x\) are both positive, in this case \(x-es\) cancel out each other and we would have \(y=|x+3|+|4-x|=x+3+4-x=7\). Both \(x+3\) and \(4-x\) are positive in the range \(-3<{x}<4\) (\(x+3>0\) --> \(x>-3\) and \(4-x>0\) --> \(x<4\)).

Let's first solve |x+3|+|4-x|=7 to answer "when is this true ?"

You can solve algebraically but it is much easier to do it using a simple number line approach. Remember |x-a| means distance between x and a on the number line Here the two points in question are -3 and 4 Now it is easy to imagine the three cases that x is to the left of -3, between -3 and 4 and to the right of 4. The only case when the two distances add up to the distance between -3 and 4, ie, 7 is case two. In case 1 and 3, the sum will exceed 7

1) could mean case 2 or 3. Not sufficient 2) could mean case 1 or 2. Not sufficient 1+2) can only mean case 2. Sufficient to know that y=7

Guys, the be low is my approcah for any modulus qtn in GMAT.

Remember. The meaning of |x-y| is "On the number line, the distance of X from +Y" The meaning of |x+y| is "On the number line, the distance of X from -Y" The meaning of |x| is "On the number line, the distance of X from 0".

Qtn:

for integers X and Y, If y=|x+3| + |4-x|, does y equals 7 ==> is the SUM of the distance b/e x and -3 , and x and 4 equals to 7? ==> .........-3......0...........4..... observe that X has to be anywhere b/w -3 and 4 or on any of these points for the total distance to be 7

Stmnt1: X < 4: Answer could be Yes if X is < 4 and b/w -3 and 4 but from the given information (i.e X<4) X could be some where left to -3 in which case the total distance would be > 7 hence insufficient.

......X....-3......0..........4 answer to the qtn: NO or ............-3...X...0.........4 answer to the qtn: YES

Stmnt2: X > -3: Answer could be Yes if X is > -3 and b/w -3 and 4 but from the given information (i.e X>-3) X could be some where right to 4 in which case the total distance would be > 7 hence insufficient. ..........-3......0..........4...X... answer to the qtn: NO or ..........-3...X...0.........4 answer to the qtn: YES

1&2

X must be b/w -3 and 4 ..........-3.X.X.X...0.X.X.X.X.X...4...... answer is always YES..hence Sufficient.

(1) If x = 3, y = |3+3| + |4-3| = 7. If x = -100, then y = 97 + 104 = 201. (2) If x = -2, y = 1 + 6 = 7. If x = 100, then y = 103 + 96 = 199.

Putting them together, you can quickly check every integer value of x from -3 to 4 and see that y = 7 for every one. It's only 6 values to check, you can do it very quickly in your head.

Re: If x and y are integers and y=|x+3| + |4-x|, does y equals 7 [#permalink]

Show Tags

26 May 2012, 07:38

At bunuel,

A. x<{-3} --> y=| x + 3| +|4-x| =-x-3+4-x=-2x+1, which means that when x is in the range {-infinity,-3} the value of y is defined by x (we would have multiple choices of y depending on x from the given range);

B. -3\leq{x}\leq{4} --> y=|x+3|+|4-x|=x+3+4-x=7, which means that when x is in the range {-3,4} the value of y is 7 (value of y does not depend on value of x, when x is from the given range);

C. x>{4} --> y=|x+3|+|4-x|=x+3-4+x=2x-1, which means that when x is in the range {4, +infinity} the value of y is defined by x (we would have multiple choices of y depending on x from the given range).

I understand the how you got the check points -3 and 4 but I am having a hard time understanding how to decide sign for x when you are removing absolute value symbol for example for (A) x<-3 y=| x + 3| +|4-x| how did you decide sign of "x" here ===> -x-3+4-x -2x+1

A. x<{-3} --> y=| x + 3| +|4-x| =-x-3+4-x=-2x+1, which means that when x is in the range {-infinity,-3} the value of y is defined by x (we would have multiple choices of y depending on x from the given range);

B. -3\leq{x}\leq{4} --> y=|x+3|+|4-x|=x+3+4-x=7, which means that when x is in the range {-3,4} the value of y is 7 (value of y does not depend on value of x, when x is from the given range);

C. x>{4} --> y=|x+3|+|4-x|=x+3-4+x=2x-1, which means that when x is in the range {4, +infinity} the value of y is defined by x (we would have multiple choices of y depending on x from the given range).

I understand the how you got the check points -3 and 4 but I am having a hard time understanding how to decide sign for x when you are removing absolute value symbol for example for (A) x<-3 y=| x + 3| +|4-x| how did you decide sign of "x" here ===> -x-3+4-x -2x+1

Similarly can u also explain for (B) and (C)

thank you!

-K

Absolute value properties: When \(x\leq{0}\) then \(|x|=-x\), or more generally when \(some \ expression\leq{0}\) then \(|some \ expression|\leq{-(some \ expression)}\). For example: \(|-5|=5=-(-5)\);

When \(x\geq{0}\) then \(|x|=x\), or more generally when \(some \ expression\geq{0}\) then \(|some \ expression|\leq{some \ expression}\). For example: \(|5|=5\);

So, for example if \(x<-3\) then \(x+3<0\) and \(4-x>0\) which means that \(|x+3|=-(x+3)\) and \(|4-x|=4-x\) --> \(|x+3|+|4-x|=-(x+3)+4-x=-2x+1\).

\(y=|x+3|+|4-x|\) two check points: \(x=-3\) and \(x=4\) (check point: the value of \(x\) when expression in || equals to zero), hence three ranges to consider:

A. \(x<{-3}\) --> \(y=| x + 3| +|4-x| =-x-3+4-x=-2x+1\), which means that when \(x\) is in the range {-infinity,-3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range);

B. \(-3\leq{x}\leq{4}\) --> \(y=|x+3|+|4-x|=x+3+4-x=7\), which means that when \(x\) is in the range {-3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range);

C. \(x>{4}\) --> \(y=|x+3|+|4-x|=x+3-4+x=2x-1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range).

Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {-3,4}

(1) \(x<4\) --> not sufficient (\(x<4\) but we don't know if it's \(\geq{-3}\)); (2) \(x>-3\) --> not sufficient (\(x>-3\) but we don't know if it's \(\leq{4}\));

(1)+(2) \(-3<x<4\) exactly the range we needed, so \(y=7\). Sufficient.

Answer: C.

OR: looking at \(y=|x+3|+|4-x|\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4-x\) are both positive, in this case \(x-es\) cancel out each other and we would have \(y=|x+3|+|4-x|=x+3+4-x=7\). Both \(x+3\) and \(4-x\) are positive in the range \(-3<{x}<4\) (\(x+3>0\) --> \(x>-3\) and \(4-x>0\) --> \(x<4\)).

Hope it's clear.

inequalities are posing problems! - one doubt - when it is said "-3<x<4", in this range shouldn't we check -2, -1 or 2,1 etc and see what is the value for y? is y independent of x when x<0?

\(y=|x+3|+|4-x|\) two check points: \(x=-3\) and \(x=4\) (check point: the value of \(x\) when expression in || equals to zero), hence three ranges to consider:

A. \(x<{-3}\) --> \(y=| x + 3| +|4-x| =-x-3+4-x=-2x+1\), which means that when \(x\) is in the range {-infinity,-3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range);

B. \(-3\leq{x}\leq{4}\) --> \(y=|x+3|+|4-x|=x+3+4-x=7\), which means that when \(x\) is in the range {-3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range);

C. \(x>{4}\) --> \(y=|x+3|+|4-x|=x+3-4+x=2x-1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range).

Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {-3,4}

(1) \(x<4\) --> not sufficient (\(x<4\) but we don't know if it's \(\geq{-3}\)); (2) \(x>-3\) --> not sufficient (\(x>-3\) but we don't know if it's \(\leq{4}\));

(1)+(2) \(-3<x<4\) exactly the range we needed, so \(y=7\). Sufficient.

Answer: C.

OR: looking at \(y=|x+3|+|4-x|\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4-x\) are both positive, in this case \(x-es\) cancel out each other and we would have \(y=|x+3|+|4-x|=x+3+4-x=7\). Both \(x+3\) and \(4-x\) are positive in the range \(-3<{x}<4\) (\(x+3>0\) --> \(x>-3\) and \(4-x>0\) --> \(x<4\)).

Hope it's clear.

MOD questions always floor me. Could you please suggest some good material on MODs?

\(y=|x+3|+|4-x|\) two check points: \(x=-3\) and \(x=4\) (check point: the value of \(x\) when expression in || equals to zero), hence three ranges to consider:

A. \(x<{-3}\) --> \(y=| x + 3| +|4-x| =-x-3+4-x=-2x+1\), which means that when \(x\) is in the range {-infinity,-3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range);

B. \(-3\leq{x}\leq{4}\) --> \(y=|x+3|+|4-x|=x+3+4-x=7\), which means that when \(x\) is in the range {-3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range);

C. \(x>{4}\) --> \(y=|x+3|+|4-x|=x+3-4+x=2x-1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range).

Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {-3,4}

(1) \(x<4\) --> not sufficient (\(x<4\) but we don't know if it's \(\geq{-3}\)); (2) \(x>-3\) --> not sufficient (\(x>-3\) but we don't know if it's \(\leq{4}\));

(1)+(2) \(-3<x<4\) exactly the range we needed, so \(y=7\). Sufficient.

Answer: C.

OR: looking at \(y=|x+3|+|4-x|\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4-x\) are both positive, in this case \(x-es\) cancel out each other and we would have \(y=|x+3|+|4-x|=x+3+4-x=7\). Both \(x+3\) and \(4-x\) are positive in the range \(-3<{x}<4\) (\(x+3>0\) --> \(x>-3\) and \(4-x>0\) --> \(x<4\)).

Hope it's clear.

Thanks for the great explanation . I got this answer when I tackled it using the same approach .. but got an E when I tried to tackle it in the +/- (x+3)=+/-(4-x) . I found y = +7 , -7 , 2x-1 , -2x+1 , and on plugging values that satisfy the 2 statements together it turned out to a range of -5 to 5 . Could you please guide ? Thanks a million
_________________

\(y=|x+3|+|4-x|\) two check points: \(x=-3\) and \(x=4\) (check point: the value of \(x\) when expression in || equals to zero), hence three ranges to consider:

A. \(x<{-3}\) --> \(y=| x + 3| +|4-x| =-x-3+4-x=-2x+1\), which means that when \(x\) is in the range {-infinity,-3} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range);

B. \(-3\leq{x}\leq{4}\) --> \(y=|x+3|+|4-x|=x+3+4-x=7\), which means that when \(x\) is in the range {-3,4} the value of \(y\) is \(7\) (value of y does not depend on value of \(x\), when \(x\) is from the given range);

C. \(x>{4}\) --> \(y=|x+3|+|4-x|=x+3-4+x=2x-1\), which means that when \(x\) is in the range {4, +infinity} the value of \(y\) is defined by \(x\) (we would have multiple choices of \(y\) depending on \(x\) from the given range).

Hence we can definitely conclude that \(y=7\) if \(x\) is in the range {-3,4}

(1) \(x<4\) --> not sufficient (\(x<4\) but we don't know if it's \(\geq{-3}\)); (2) \(x>-3\) --> not sufficient (\(x>-3\) but we don't know if it's \(\leq{4}\));

(1)+(2) \(-3<x<4\) exactly the range we needed, so \(y=7\). Sufficient.

Answer: C.

OR: looking at \(y=|x+3|+|4-x|\) you can notice that \(y=7\) (\(y\) doesn't depend on the value of \(x\)) when \(x+3\) and \(4-x\) are both positive, in this case \(x-es\) cancel out each other and we would have \(y=|x+3|+|4-x|=x+3+4-x=7\). Both \(x+3\) and \(4-x\) are positive in the range \(-3<{x}<4\) (\(x+3>0\) --> \(x>-3\) and \(4-x>0\) --> \(x<4\)).

Hope it's clear.

Thanks for the great explanation . I got this answer when I tackled it using the same approach .. but got an E when I tried to tackle it in the +/- (x+3)=+/-(4-x) . I found y = +7 , -7 , 2x-1 , -2x+1 , and on plugging values that satisfy the 2 statements together it turned out to a range of -5 to 5 . Could you please guide ? Thanks a million

Could you please elaborate the red part?
_________________

I mean that combining both statements x is between -3 and 4 , so I plugged all the values in this range in both 2x-1 and -2x+1 giving the range of Ys -5 to 5
_________________

I mean that combining both statements x is between -3 and 4 , so I plugged all the values in this range in both 2x-1 and -2x+1 giving the range of Ys -5 to 5

y is equal to 1-2x only when x<-3. y is equal to 2x-1 only when x>4.

When -3<x<4, then y is equal to 7.
_________________

Hi guys, I would like to deeply understand how to deal with absolute value questions like the one attached. Thank you very much

The Expression given in the Question is Y = lx+3l + l4-xl .. & Question asks Is Y = 7 ????

Statement 1 :: x<4 ..... when we plugin any value of x less than 4 till -3 we will get a result as Y = 7 but below -3 ... Y will not be equal to 7 . Therefore, Insufficient.

Similarly, Statement :: 2 .... is insufficient.......

with 1+2 ..... we get the value of x in between 4 & -3 ...... i.e., -3<x<4 ....... For all the value of x in between -3 & 4 ... the value of

Y is always. 7 .. Therefore, Sufficient....

Hence, C ...........
_________________

If you don’t make mistakes, you’re not working hard. And Now that’s a Huge mistake.

gmatclubot

Re: Algebra->Inequalities (Absolute Value)
[#permalink]
07 May 2013, 20:08

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Since my last post, I’ve got the interview decisions for the other two business schools I applied to: Denied by Wharton and Invited to Interview with Stanford. It all...

Marketing is one of those functions, that if done successfully, requires a little bit of everything. In other words, it is highly cross-functional and requires a lot of different...