Is a/b < 1/2 ?
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Source: Beat The GMAT — Data Sufficiency |
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fibbonnaci
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from the question: is 2a <b ?
statement 1)
2a+1<b
pick numbers. say a=2
so b>5. say b=6
then 2a < b. check for other numbers such as negative numbers and zero. you will find it satisfiees the statement.
Sufficient.
Statement 2)
2a-2<b
say a=2,
b>2. say b=3
then 2a> b
but if b=6, then 2a< b.
therefore insufficient.
IMO
A
statement 1)
2a+1<b
pick numbers. say a=2
so b>5. say b=6
then 2a < b. check for other numbers such as negative numbers and zero. you will find it satisfiees the statement.
Sufficient.
Statement 2)
2a-2<b
say a=2,
b>2. say b=3
then 2a> b
but if b=6, then 2a< b.
therefore insufficient.
IMO
A
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fibbonnaci
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oops sorry i missed that..
we need to answer whether a/b < 0.5
statement 1:
a/(b-1) <1/2
if b is positive, (b-1)<b
if a/(b-1) is less than half then a number with greater denominator b should definitely give less than half(coz the numerators are the same).
you can check by plugging in numbers.
say a=1 and b=4,
a/(b-1) = 1/3 which is less than 1/2.
then a/b= 1/4 which is less than 0.5
Now consider b is negative and a is also negative.
say a= -1 and b= -2
then according to the equation a/(b-1) = 1/3 which is less than 1/2,
but a/b= 1/2 which is equal to half.
Therefore insufficient.
Statement 2:
(a-1)/b <0.5
say a= 2 and b= 3
then 1/3< 1/2 but a/b > 1/2.
lets check another value: a=3 and b=6
2/6 < 1/2 but a/b= 1/2. Thus insufficient.
combining both:
we need to plug in numbers that satisfy both the equations
say a=1 and b=4
then a/b<1/2
similarly say a=-1 and b= -5
then too a/b <1/2.
sufficient.
we need to answer whether a/b < 0.5
statement 1:
a/(b-1) <1/2
if b is positive, (b-1)<b
if a/(b-1) is less than half then a number with greater denominator b should definitely give less than half(coz the numerators are the same).
you can check by plugging in numbers.
say a=1 and b=4,
a/(b-1) = 1/3 which is less than 1/2.
then a/b= 1/4 which is less than 0.5
Now consider b is negative and a is also negative.
say a= -1 and b= -2
then according to the equation a/(b-1) = 1/3 which is less than 1/2,
but a/b= 1/2 which is equal to half.
Therefore insufficient.
Statement 2:
(a-1)/b <0.5
say a= 2 and b= 3
then 1/3< 1/2 but a/b > 1/2.
lets check another value: a=3 and b=6
2/6 < 1/2 but a/b= 1/2. Thus insufficient.
combining both:
we need to plug in numbers that satisfy both the equations
say a=1 and b=4
then a/b<1/2
similarly say a=-1 and b= -5
then too a/b <1/2.
sufficient.
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eaakbari
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I realize I did make a mistake with my calculation, C is the correct answer but I still feel this method of plugging is too time-consuming and convoluted or was that just me?fibbonnaci wrote:oops sorry i missed that..
we need to answer whether a/b < 0.5
statement 1:
a/(b-1) <1/2
if b is positive, (b-1)<b
if a/(b-1) is less than half then a number with greater denominator b should definitely give less than half(coz the numerators are the same).
you can check by plugging in numbers.
say a=1 and b=4,
a/(b-1) = 1/3 which is less than 1/2.
then a/b= 1/4 which is less than 0.5
Now consider b is negative and a is also negative.
say a= -1 and b= -2
then according to the equation a/(b-1) = 1/3 which is less than 1/2,
but a/b= 1/2 which is equal to half.
Therefore insufficient.
Statement 2:
(a-1)/b <0.5
say a= 2 and b= 3
then 1/3< 1/2 but a/b > 1/2.
lets check another value: a=3 and b=6
2/6 < 1/2 but a/b= 1/2. Thus insufficient.
combining both:
we need to plug in numbers that satisfy both the equations
say a=1 and b=4
then a/b<1/2
similarly say a=-1 and b= -5
then too a/b <1/2.
sufficient.
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jerryragland
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Guys, correct me if I am wrong
To find is 2a < b?
(1) a/(b - 1) < 1/2
2a < b - 1 ==> 2a + 1 < b ==> so 2a < b -- 1 Sufficient
(2) (a - 1)/b < 1/2
2a - 2 < b ==> but can not say 2a < b -- 2 Not sufficient
Hence a.
To find is 2a < b?
(1) a/(b - 1) < 1/2
2a < b - 1 ==> 2a + 1 < b ==> so 2a < b -- 1 Sufficient
(2) (a - 1)/b < 1/2
2a - 2 < b ==> but can not say 2a < b -- 2 Not sufficient
Hence a.
