BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
RedeemTarget Test Prep · GMAT
Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.
with Chris Peckover
with Logan Thompson
Complete access from day one. Study on your schedule.
Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.
when would y be zero? If |x|+x=0, then x=-|x|. Since an absolute value is ≥0, this means that y will equal zero if x is negative (or zero).zaarathelab wrote:If y is an integer and y=|x|+x, is y=0?
1) x<0
2) y<1
Hello Geva,Geva@MasterGMAT wrote:when would y be zero? If |x|+x=0, then x=-|x|. Since an absolute value is ≥0, this means that y will equal zero if x is negative (or zero).zaarathelab wrote:If y is an integer and y=|x|+x, is y=0?
1) x<0
2) y<1
another way to look at the same is that for |x|+x to equal zero, the x has to be negative to counter the "positive" of |x|.
This is why stat. (1) is sufficient: if x<0, then y=0 for any value of x.
Stat. (2): y is an integer, so if it's smaller than 1, it has to be either zero or negative. we've already seen that if x is negative, y is equal to zero. Can we find a negative y? No way: for y to be negative, something needs to "drag" |x|+x below the zero line. Since |x| is non-negative, x has to be negative for that to happen - and we've already seen that a negative x still only gets y=0. So stat. (2) is sufficient as well.
Note that if the stem did not say y is an integer, we could use x=1/4 to find y=|1/4|+1/4 =1/2 to be smaller than 1 but not zero. The statement is only sufficient because y has to be an integer <1: zero or negative.
sl750 wrote:Geva@MasterGMAT wrote:when would y be zero? If |x|+x=0, then x=-|x|. Since an absolute value is ≥0, this means that y will equal zero if x is negative (or zero).zaarathelab wrote:If y is an integer and y=|x|+x, is y=0?
1) x<0
2) y<1
another way to look at the same is that for |x|+x to equal zero, the x has to be negative to counter the "positive" of |x|.
This is why stat. (1) is sufficient: if x<0, then y=0 for any value of x.
Stat. (2): y is an integer, so if it's smaller than 1, it has to be either zero or negative. we've already seen that if x is negative, y is equal to zero. Can we find a negative y? No way: for y to be negative, something needs to "drag" |x|+x below the zero line. Since |x| is non-negative, x has to be negative for that to happen - and we've already seen that a negative x still only gets y=0. So stat. (2) is sufficient as well.
Note that if the stem did not say y is an integer, we could use x=1/4 to find y=|1/4|+1/4 =1/2 to be smaller than 1 but not zero. The statement is only sufficient because y has to be an integer <1: zero or negative.
Hello Geva,
If y<1, then we can have two cases 0<y<1 or y<=0. In this case x will be a positive fraction and y will NOT be equal to 0
New here Create free account
