The answers below may be incorrect. I haven't matched them with OA. If you see any problem with the logic or answer; please comment.

Bunuel wrote:

1. An integer greater than 1 that is not prime is called composite. If the two-digit integer n is greater than 20, is n composite?

(1) The tens digit of n is a factor of the units digit of n.

(2) The tens digit of n is 2.

Sol:

20<n<100

(1)

Possible values of n:

22,24,26,28 ; Between 21 and 29, inclusive; 2 is a factor of 2,4,6,8

30,33,36,39 ; Between 30 and 39, inclusive; 3 is a factor of 0,3,6,9

40,44,48; Between 40 and 49, inclusive; 4 is a factor of 0,4,8

50,55

60,66

70,77

80,88

90,99

Every possible value is composite. Sufficient.

(2)

Unit's digit can be 3 or 6 giving at least 2 possibilities; 23 or 26, one of which is prime and other composite.

Not sufficient.

Ans: "A"

Bunuel wrote:

2. Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

(1) Two of the interior angles of ABCD are right angles.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

Sol:

(1) If the opposite angles are \(90^{\circ}\), then the quadrilateral is a rectangle or square. None of the interior angles is \(60^{\circ}\)

If the adjacent angles are \(90^{\circ}\), then the quadrilateral may have the rest two angles are any set of supplementary angles which also includes {60,120}. Maybe one of the interior angles is \(60^{\circ}\). Not sure though.

Not sufficient.

(2) The adjacent angles are \(90^{\circ}\), then the quadrilateral may have the rest two angles be any set of supplementary angles which also includes {60,120}. Maybe one of the interior angles is \(60^{\circ}\). Not sure though.

Not sufficient.

Combing both;

Two interior angles are \(90^{\circ}\). They can't be opposite angles as there are also two angles that are in ratio 1:2. If two angles are 90. Then their sum is 180. Sum of all interior angles of a quadrilateral is 360. The sum of the other two angles is 180.

Also they are in ratio;

1/2

So; x+2x=180

x=60

2x=120.

For sure there is one angle which is \(60^{\circ}\)

Sufficient.

Ans: "C"

Bunuel wrote:

3. Is x + y < 1 ?

(1) x < 8/9

(2) y < 1/8

Sol:

(1) x<8/9

y can be 1000 or 1/1000.

Not sufficient.

(2)y<1/8

x can be 1000 or 1/1000.

Not sufficient.

Combing both;

\(x+y < \frac{8}{9} + \frac{1}{8}\)

\(x+y < \frac{73}{72}\)

x+y can be 722/720 or 1/16.

Not sufficient.

Ans: "E"

Bunuel wrote:

4. Is x^4 + y^4 > z^4 ?

(1) x^2 + y^2 > z^2

(2) x+y > z

Sol:

(1)

\(x^2+y^2 > z^2\)

Squaring both sides

\(x^4+y^4+2x^2y^2 > z^4\)

Now,

\(2x^2y^2\) will always be equal to or greater than 0 because square is always +ve. "+ve*+ve*2" will always be positive or greater than equal to 0.

Hence;

\(x^4+y^4>z^4\)

Sufficient.

(2)

x+y > z

I don't know the formula for double squaring this one. So; just substituting some values;

-1-1>-10

-2>-10

16<10000

2+2>1

16+16>1

32>1

Not Sufficient.

Ans: "A"

Bunuel wrote:

5. At a certain theater, the cost of each adult's ticket is $5 and the cost of each child's ticket is $2. What was the average cost of all the adult's and children's tickets sold at the theater yesterday?

(1) Yesterday ratio of # of children's ticket sold to the # of adult's ticketr sold was 3 to 2

(2) Yesterday 80 adult's tickets were sold at the theater.

Sol:

Adult's ticket sold: a

Children's ticket sold: c

Total Price: 5a+2c

Average Cost:

(1)

\(\frac{c}{a}=\frac{3}{2}\)

\(2c=3a\)

\(c=(3/2)a\)

\(\frac{(5a+2c)}{(a+c)}=\frac{5a+3a}{a+(3/2)a}=\frac{16}{3}\)

Sufficient.

(2)

80 adult tickets were sold doesn't tell us anything about the number of children's tickets sold.

Not Sufficient.

Ans: "A"

Bunuel wrote:

6. Are some goats not cows?

(1) All cows are lions

(2) All lions are goats.

Sol:

(1) Not sufficient. Doesn't tell us anything about goats.

(2) Not sufficient. Doesn't tell us anything about cows.

Combining both;

We know that all cows are goats as well as lions. But; there are also few lions that are not cows but goat. Thus, some goats are not cows; they are lions.

Sufficient.

Ans: "C"

Bunuel wrote:

7. Patrick is cleaning his house in anticipation of the arrival of guests. He needs to vacuum the floors, fold the laundry, and put away the dishes after the dishwasher completes its cycle. If the dishwasher is currently running and has 55 minutes remaining in its cycle, can Patrick complete all of the tasks before his guests arrive in exactly 1 hour?

(1) Vacuuming the floors and folding the laundry will take Patrick 36 minutes.

(2) Putting away the dishes will take Patrick 7 minutes.

Sol:

(1) Not Sufficient. Putting away the dishes may take less than 5 minutes or more than 5 minutes.

(2) Sufficient. Irrespective of how long it takes for vacuuming or laundry, putting away the dishes alone will cross the 1 hour deadline. 55 minutes will be spent washing and say Pat is already done done with his laundry and vacuuming; he can't complete all his tasks before at least 1hour 2minutes > 1hour.

Ans: "B"

Bunuel wrote:

8. Are all of the numbers in a certain list of 15 numbers equal?

(1) The sum of all the numbers in the list is 60.

(2) The sum of any 3 numbers in the list is 12.

Sol:

(1)

There can be fifteen 4's making the sum=60 and all of the elements equal.

There can be fourteen 1's and one 46 making the sum=60 and not all elements equal.

Not Sufficient.

(2)

Don't know by what principle of mathematics it is so. But; looks like it is possible only when all of them are 4.

Sufficient.

Ans: "B"

Thanks for the post Bunuel.

_________________

~fluke

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