Neither 1 nor 2 is sufficient. The x could be negative in either case 1 or 2. If x is negative and y is not, the product will surely be less than 16.

for xy > 16 , x and y should have similar signs.

1) 1 < |x| < 4 means that x can be either (-1.2,-1.3,-1.4.......,-3.9) or x can be (1.1,1.2,1.3....,3.9) and value of y is not provided hence not sufficient.

2) y > 16 provides us the value of y but we donot know the value of x. hence not sufficient.

Combining 1 and 2 we are not sure about the sign of x as x can be +ve or -ve.

Thus E is the answer.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is xy > 16?

(1) 1 < |x| < 4
(2) y > 16


In the original condition, there are 2 variables(x,y), which should match with the number of equations. So you need 2 equations. However, for 1) 1 equation, for 2) 1 equation, which is likely to make C the answer. When 1) & 2), x=2, y=18 -> yes, x=-2, y=18 -> no, which is not sufficient.
Therefore, the answer is E.


 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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St1:
value of x can be anything from -1.1 to -3.9 or 1.1 to 3.9
and there is no clue about y
Insufficient

St:2 y>16
if x = 2 then xy = 32 > 16
if x = -2 then xy = -32<16
insufficient

St 1+2:
still value of x is not clear

This Ans: E

1) No info about Y......Insuf

2) No info about X......Insuf


Combine 1&2

X=2 Y= 17.....XY=34>16

X=-2 Y=17.....XY=-34<16

Answer: E

Here's My solution

Stem: Is XY > 16. (Note: No constraints given. Both X and y could be positive, Negative, Zero, Integer, Non integer)

S1: 1 < |x| < 4
Tells us X = any number on the number line between 1 and 4 or any number on number line between -1 and -4. Also no information on Y.
Insuff

S2: Y > 16
Tells us Y could be anything from 16 to Infinity. However no info on X. If X = 0 or negative XY is less then 16 and if X is 1, XY = 16 and if X is positive and greater then 1 XY is greater then 16.
Insuff

S1+S2: X is any number on the number line between 1 and 4 or -1 and -4. Y is greater then 16. XY is less then 16 is X is negative. Its more then 16 if x is positive.
Insuff

Final Answer : E


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Is \(xy > 16\)?

\((1) 1 < |x| < 4\)

This equation does not tell us anything about \(y\) and \(y\) can take any possible value.

Hence, (1) =====> is NOT SUFFICIENT

\((2) y > 16\)

This equation does not tell us anything about \(x\) and \(x\) can take any possible value.

Hence, (2) =====> is NOT SUFFICIENT

Combining (1) & (2)

We know y > 16

And, x can be -3, -2 or 3 & 2

As x can take both positive and negative values, the we will get answer to the question \(xy > 16\) as TRUE and FALSE

Hence, Combined (1) & (2) =====> is NOT SUFFICIENT

Hence, Answer is E
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Statement 1) 1 < |x| < 4

No information about Y. Insufficient. AD BCE

Statement 2) Y > 16

No information about X. Insufficient. B CE

Using 1 and 2.

X = -1 and Y=20; Thus XY < 16
or
X = 2 and Y=20; XY = 40; Thus XY > 16

Answer is E

I got it wrong.

Question: Is xy > 16?

To get this, we need to prove that both x and y have the same sign.

St 1: 1 < |x| < 4

means x can be in between 1 & 4 or -1 & -4

Also we don't know what "y" is? Not Sufficient

St 2: y > 16

As we don't know anything about "x", it is Not Sufficient

Combining St 1 & 2 we don't whether xy > 16

If x is in between 1& 4, answer is YES

If x is in between -1 & -4, answer is NO.

(E)
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Target question: Is xy > 16?

Statement 1: 1 < |x| < 4
Since there's no information about y, we cannot determine whether xy is greater than 16
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: y > 16
Since there's no information about x, we cannot determine whether xy is greater than 16
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several values of x and y that satisfy BOTH statements. Here are two:
Case a: x = 2 and y = 20, in which case xy = 40. In this case, the answer to the target question is YES, xy IS greater than 16
Case b: x = -2 and y = 20, in which case xy = -40. In this case, the answer to the target question is NO, xy is NOT greater than 16
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
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For XY to be greater than 16 , its imperative for both X and Y to be positive. The digit value of both also determine the product.

Statement 1 : We get the mod value of X , neither are we sure if X is positive or negative nor are we sure about the sign/ digit value of Y.
Statement 2 : Even if Y is greater than 16 we cant tell about X from this statement.

Combined : Due to uncertainty of the sign value of X we cant come to a conclusion and hence E is the answer

doesnt this statement tells us that X is positive? given the fact that it is between 1 and 3, both positive,
1) 1 < |x| < 4

why are we considering negative values for X ?

Is xy > 16?

(1) 1 < |x| < 4
(2) y > 16


(1) 1< |x| < 4 means,
1< x < 4 or -1 > x > -4. It says, value of x is between 1 & 4 and -1 & -4. NOT SUFFICIENT.

(2) only value of y is given

(1) + (2), Will get two values of x.

Thus correct option E
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