If ab = 3, is a b ? (1) b ≤ 1.5 (2) a ≥ 2

Question

If ab = 3, is a > b ?

(1) b ≤ 1.5 
(2) a ≥ 2

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yashikaaggarwal · Answer

ab = 3, is a > b ?

(1) b ≤ 1.5
Case 1: B = 1.5
A = 2 {A>B}

Case 2: B = -1.5
A = -2 {A<B}
(Insufficient)

(2) a ≥ 2
A = 2
B = 1.5

A = 3
B = 1 
B will be smaller than A every time.
(Sufficient)

IMO B

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anthien128 · Answer

IMO B is the correct answer. (1) Since b ≤ 1.5, b may be negative or positive number. We can solve this question by taking example. If b is positive number then we have a = 3/b. Since 0 < b ≤ 1.5 then a ≥ 2 > 1.5 ≥ b. This is sufficient. If b is negative number. - For example, b = -3 then a = -1. In this case, a > b - For example, b = -1 then a = -3. In this case, a < b In both cases, we cannot conclude which number is bigger, a or b. Therefore (1) is INSUFFICIENT. (2) Since b = 3/a and a ≥ 2 > 0 then b ≤ 1.5. Therefore a ≥ 2 > 1.5 ≥ b. This option is SUFFICIENT.

sood1596 · Answer

Question: ab=3; is a>b?

1)
b<=1.5

Case1: b=1.5 a=2 ; a>b YES
Case2: b=-1.5 a=-2; a>b NO
Not sufficient

2)
a>=2
For all cases a will be greater than b
Sufficient

Answer - B

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 • ab = 3
• We need to find if a > b

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:  b ≤ 1.5
 • According to this statement, b can be either negative or positive. Now, lets consider the following two cases:
 o Case 1: b = 1 and a = 3,
  In this case a*b = 3 and b < a 
o Case 2: b = -1 and a = -3,
  In this case a*b = 3 and b > a  
• We are getting contradictory results. 
Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D.

Statement 2:  a ≥ 2
 • According to this statement: a ≥ 2
 o It means a is positive so b must be positive too. 
• Now, a ≥ 2 ⟹ ab ≥ 2b ⟹ 3 ≥ 2b ⟹ b ≤ 1.5.
 o Since, b is positive so, the range of b is 0 ≤ b ≤ 1.5
o Thus, b is always less than a, as a ≥ 2.  
Hence, statement 2 is sufficient.
Thus, the correct answer is  Option B.

KaramveerBakshi · Answer

ab = 3 Is a>b? Statements: (1) b≤1.5 b can also be negative. We can have 2 cases; b = 1.5, a = 2. a>b. OR b = -1.5, a = -2. ab (Always) Sufficient. Hence, the answer is Option (D).

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If ab = 3, is a > b ? (1) b ≤ 1.5 (2) a ≥ 2

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