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GMAT PREP DS
Source: Beat The GMAT — Data Sufficiency |
Sure, sorry I just noticed the characters above. Here's the question:
Is absolute value x-y > absolute value x - absolute value y?
1) y < x
2) xy < 0
I also have another question please ( looked at the other forums but did not find any answer helpful):
If the operation * is defined for all integers a & b by a*b = a +b -ab, which of the following statements must be true for all integers a, b and c?
I)a*b=b*a
II)a*0=a
III)(a*b)@c =a*(b*c)
Thank you!
Is absolute value x-y > absolute value x - absolute value y?
1) y < x
2) xy < 0
I also have another question please ( looked at the other forums but did not find any answer helpful):
If the operation * is defined for all integers a & b by a*b = a +b -ab, which of the following statements must be true for all integers a, b and c?
I)a*b=b*a
II)a*0=a
III)(a*b)@c =a*(b*c)
Thank you!
i will try to say something about 2 problem
If the operation * is defined for all integers a & b by a*b = a +b -ab, which of the following statements must be true for all integers a, b and c?
I)a*b=b*a
II)a*0=a
III)(a*b)@c =a*(b*c
here i don`t see any way other then checking all variants
1) a*b=a+b-ab, b*a=b+a-ba, does a+b-ab=b+a-ab, yes you can cancel all variables and left with 0=0
2)a*0=a+0-a0=a. does a=a. yes
3) rather long way
let it be a*b=x
x*c=x+c-cx=(a+b-ab)+c-c(a+b-ab)=a+b-ab+c-ca-cb+cab
let it be b*c=y
a*y=a+y-ay=a+(b+c-bc)-a(b+c-bc)=a+b+c-bc-ab-ac+abc
both bolded parts are identical
so the answer is all three
If the operation * is defined for all integers a & b by a*b = a +b -ab, which of the following statements must be true for all integers a, b and c?
I)a*b=b*a
II)a*0=a
III)(a*b)@c =a*(b*c
here i don`t see any way other then checking all variants
1) a*b=a+b-ab, b*a=b+a-ba, does a+b-ab=b+a-ab, yes you can cancel all variables and left with 0=0
2)a*0=a+0-a0=a. does a=a. yes
3) rather long way
let it be a*b=x
x*c=x+c-cx=(a+b-ab)+c-c(a+b-ab)=a+b-ab+c-ca-cb+cab
let it be b*c=y
a*y=a+y-ay=a+(b+c-bc)-a(b+c-bc)=a+b+c-bc-ab-ac+abc
both bolded parts are identical
so the answer is all three
as for the first prblem, it was recently been discussed. follow below link
https://www.beatthegmat.com/modulus-and- ... 81958.html
https://www.beatthegmat.com/modulus-and- ... 81958.html
