Is xy > 5? (1) 1 <= x <= 3 and 2 <= y <= 4 (2) x + y = 5

SOLUTION

Is xy > 5?

(1) \(1\leq{x}\leq{3}\) and \(2\leq{y}\leq{4}\)
(2) x + y = 5

Probably the easiest way to tackle this problem is to pick numbers. Quite easy to get both an YES and a NO answers:

x = 1 and y = 4 --> xy = 4 < 5;
x = 3 and y = 2 --> xy = 6 > 5.

Answer: E.
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Sol:St 1: Given \(1\leq{x}\leq{3}\) and \(2\leq{y}\leq{4}\)

Note x and y can have any values (not only integer) in this range.

So x =1 , y=4 the answer to the question is NO
But if x=2, y=3 then answer is YES.

So A and D ruled out
St 2: x+y=5 the above values can be used.
So not enough
B ruled out

Let x=1.1, y=3.9 then xy is less than 5
but if x=2 and y=3 then xy is greater then 5.

Ans is E

Difficulty level of 650 is okay.
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Not necessary to pick decimals, lets pick simpler numbers

1+2

x=1 and y=4
is xy>5?
Answer is No

x=3 y=2
is xy>5?
Answer is Yes

Answer E
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x can take any values between 1 and 3 ( both included), y can take any values between 2 and 4 ( both included).

Please note x and y can even take decimal values.

For simplification lets work with integer values only

Statement 1 3 * 2 =6 [yes, xy > 5]
But, 2 * 2 = 4 [ No, xy is not greater than 5]

We have two answers to the questions from statement 1. Hence statement 1 is not sufficient.
Options A and D are eliminated.

Statement 2 says x + y = 5

When x = 1, y = 4 xy <5
When x = 2, y = 3 xy >5

Here, again we have two answers to our question. Hence, statement two alone is not sufficient.

Option B is eliminated.

Now, lets combine both the statements and check.

x = 1, y = 4 xy < 5
x = 3, y = 2 xy > 5

We do not have an definite answer. Both the statements together are also not sufficient.

Hence, option E

Regards,
Harish

Here, the question does not specify that the numbers are restricted only to integers. So, it can include even decimals but it is enough to consider integers in the first place.

Is xy>5?
Here, just to understand, so far from the question, we can infer that either both x & y are positive or both x & y are negative.

Statement 1:
From the range, if we assume x=2 and y=3; xy=6; we get the answer YES.
If we assume x=1 and y=2; xy=2; we get the answer NO.
Insufficient.

Statement 2:
Here, x and y can take multiple values:
x=2 and y=3; we get the answer YES.
x=1 and y=4; we get the answer NO.
There are more values possible, of course, including decimals.
Insufficient.

Combined, we have a specific range of values and still it is insufficient, as in Statement 2 example.

Ans is (E).

Is \(xy > 5?\)

(1) \(1\leq{x}\leq{3}\) and \(2\leq{y}\leq{4}\)
(2) \(x + y = 5\)

Statement 1
Given the range of values of x and y : \(1\leq{x}\leq{3}\) and \(2\leq{y}\leq{4}\)

for \(x = 3\) and \(y =4\), \(xy = 12\) or, \(xy > 5\)
for \(x = 1\) and \(y= 2\), \(xy = 2\) or, \(xy < 5\)

So, statement (1) is not sufficient.................(A)(D)

Statement 2

Given that, \(x + y = 5\) is satisfied by \((x= 1\) and \(y = 4)\) & \(( x= 2\) and \(y = 3)\)

for \(x= 1\) and \(y = 4\), \(xy = 4\) or \(xy < 5\)
for \(x= 2\) and \(y = 3\), \(xy = 6\) or \(xy > 5\)

So,statement (2) is not sufficient.................(B)

Since, the set of values in statement (2) also satisfies condition in statement (1), both statements (1) and (2) are insufficient to evaluate \(xy > 5\).

Answer: (E)

#1
value of x range from 1 to 3 and y 2 to 4 so yes and no for xy>0
#2
x+y=5
x,y can be 0,5, 2,3 ,4,1 many other options so xy>5 no

from 1 & 2
we cannot deduce anything in common
IMO E

S1: The simplest way to do this is to take the smallest of both ranges as x and y and multiple together and take the largest of the ranges and x and y and multiply them together.
a) 1*2= 2, not >5
b) 3*4=12 >5.

We have got 2 different answers, therefore A isn't sufficient, strike off A and D.

S2: let's make cases
a) 2+3 =5, 2*3=6 >5
b) 1+5=5, 1*4=4<5.

again two different answers, B is not sufficient. Strike off B.

When combining the 2 statements. Both the pressing questions still remain. therefore the final answer should be E.

Hope that's helpful.

Solution:

Question Stem Analysis:

We need to determine whether xy > 5.

Statement One Alone:

Statement one alone is not sufficient. For example, if x = 3 and y = 4, then xy = 12 > 5. However, if x = 1 and y = 2, then xy = 2 < 5.

Statement Two Alone:

Statement two alone is not sufficient. For example, if x = 2 and y = 3, then xy = 6 > 5. However, if x = 1 and y = 4, then xy = 4 < 5.

Statements One and Two Together:

Both statements together are still not sufficient (we can use the same two examples from statement two since they also satisfy statement one).

Answer: E
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Is xy > 5?

(1)
1≤x≤3: Range = {1,2,3}
and
2≤y≤4: Range = {2,3,4}
Highest (4*3 = 12) lowest (2*1=2)
this stem has both possiablities - Not Sufficient

(2) x + y = 5
- x and y can be in combination of (1,4) (2,3) if both are positive integers,
- negative or mix of (+ive and -ive), will have another different possiablities for x and y - Not Sufficient

Combination of both statement: Not Sufficient
Correct option E

Quick Tip: Try to use values to disprove sufficiency of statements

Question: Is xy > 5?

Statement 1: 1≤x≤3 and 2≤y≤4

\(xy_{min} = 1*2 = 2\) NO
\(xy_{max} = 3*4 = 12\) YES

NOT SUFFICIENT

STatement 2: x + y = 5

for x = 0 and y = 5, xy = 0 i.e. NO
for x = y = 2.5, \(xy_{max} = 2.5*2.5 = 6.25\) YES

NOT SUFFICIENT

COmbining
\(xy_{min} = 1*2 = 2\) NO
for x = y = 2.5, \(xy_{max} = 2.5*2.5 = 6.25\) YES

NOT SUFFICIENT

Answer: Option E

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