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. 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. 3. Is x + y z^4 ? (1) x^2 + y^2 > z^2 (2) x+y > z 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. 6. Are some goats not cows? (1) All cows are lions (2) All lions are goats. 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. 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. Please share your way of thinking, not only post the answers. OA and explanations to follow.

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Collection of 8 DS questions

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Jayalakshivit

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23 Jan 2013, 08:43

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Pls Help me.

In DS questions when it asks for .. IS some data followed by ? given 2 statement below.

A definite yes or definite no is sufficient for the answer. or when we should use this method ???

Bunuel

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23 Jan 2013, 08:51

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Jayalakshivit

In a Yes/No Data Sufficiency questions, statement(s) is sufficient if the answer is “always yes” or “always no” while a statement(s) is insufficient if the answer is "sometimes yes" and "sometimes no".

When a DS question asks about the value of some variable, then the statement(s) is sufficient ONLY if you can get the single numerical value of this variable.

Hope it helps.

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13 Jun 2013, 10:08

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asterixmatrix

Bunuel

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.

Please share your way of thinking, not only post the answers.

OA and explanations to follow.

Option 1 we know 2 angles are 90 degree each but we have no info about the other 2 angles which can be (60,120), (80,100) etc. hence insuff
Option 2 says angle ABC = 2 * angle BCD again insuff as we can have an angle equal to 60 degree or none of the angles as 60degree

Taking 1 and 2 we know 2 angles are 90degree each and angle ABC is twice angle BCD
lets assume angle ABC = 90 degree then angle BCD = 45. we know the 3rd angle is 90 degree so 4th angle becomes 135 (sum of angles of a quadrilateral = 360degrees) so answer will NO ( none of angles are 60degree)
now lets consider that the 1st unknown angle is twice the 2nd unknown angle (other 2 are 90 degree each) we can get value for smaller angle as 60degree
hence insuff

will go with E

Asterix
from eeek?? to Eureka!!! to eeek???

One angle is x other is 2x, x+2x =180(360-180), this gives x = 60 degree....B is correct...

Bunuel

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13 Jun 2013, 10:13

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asterixmatrix

Bunuel

One angle is x other is 2x, x+2x =180(360-180), this gives x = 60 degree....B is correct...

OA's are given here: collection-of-8-ds-questions-85290.html#p639290 OA fot this question is E, not B.

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

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

Answer: E.

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13 Jun 2013, 10:23

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By combining both we can get answer.

Two of the interior angles of ABCD are right angles. which sum of two interior angles = 180

Now fom B

The degree measure of angle ABC is twice the degree measure of angle BCD. i.e. 1:2,

X+2X + 90 + 90 = 360
3X=180
X=60

Bunuel

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13 Jun 2013, 10:26

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trafficspinners

Again OA is E, not C. Check the solution above: Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

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15 May 2014, 05:01

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Bunuel, thanks for the wonderful set, i had a question

. Is x^4 + y^4 > z^4 ?
(1) x^2 + y^2 > z^2
(2) x+y > z

x^4 + y^4 = ((x^2) + (y^2))^2 - 2*x^2*y^2

So basically we want to find out if ((x^2) + (y^2))^2 - 2*x^2*y^2 > z^4

OR if

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

Now by (1), we know that x^2 + y^2 > z^2

Or

((x^2) + (y^2))^2 > z^4 ( squaring both sides, both sides are absolutely positive)...... (a)

We also know that 2*x^2*y^2 will be less than ((x^2) + (y^2))^2......(b)

Combining (a) and (b), can we not conclude that ((x^2) + (y^2))^2 > z^4 + 2*x^2*y^2 and hence making (1) sufficient

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15 May 2014, 06:41

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gaurav1418z

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

The best way to deal with this problem is plugging numbers. Remember on DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.

(1) $x^2+y^2>z^2$
It's clear that we get YES answer very easily with big x and y (say 10 and 10), and small z (say 0).

For NO answer let's try numbers from Pythagorean triples:
$x^2=3$, $y^2=4$ and $z^2=5$ ($x^2+y^2=7>5=z^2$) --> $x^4+y^4=9+16=25=z^4$, so we have answer NO ($x^4+y^4$ is NOT more than $z^4$, it's equal to it).

Not sufficient.

(2) $x+y>z$. This one is even easier: again we can get YES answer with big x and y, and small z.

As for NO try to make z some big enough negative number: so if $x=y=1$ and $z=-5$, then $x^4+y^4=1+1=2<25=z^4$.

Not sufficient.

(1)+(2) As we concluded YES answer is easily achievable. For NO try the case of $x^2=3$, $y^2=4$ and $z^2=5$ again: $x+y=\sqrt{3}+\sqrt{4}>\sqrt{5}$ ($\sqrt{3}+2$ is more than 3 and $\sqrt{5}$ is less than 3), so statement (2) is satisfied, we know that statement (1) is also satisfied ($x^2+y^2=7>5=z^2$) and $x^4+y^4=9+16=25=z^4$. Not sufficient.

Answer: E.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-x-4-y-4-z-101358.html

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15 May 2014, 06:57

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Ok Bunuel, i shall stick to the plugging number approach, please can you confirm if both terms in an equality are positive, we can square both sides or even raise to the power of 3, without changing the inequality sign?

Bunuel

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15 May 2014, 07:10

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gaurav1418z

1. We can raise both parts of an inequality to an even power if we know that both parts of an inequality are non-negative (the same for taking an even root of both sides of an inequality)

2. We can always raise both parts of an inequality to an odd power (the same for taking an odd root of both sides of an inequality).

Adding/subtracting/multiplying/dividing inequalities: help-with-add-subtract-mult-divid-multiple-inequalities-155290.html

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asterixmatrix

Bunuel

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.

Please share your way of thinking, not only post the answers.

OA and explanations to follow.

given n >20. let N be of the form 10x + y where x is ten's digit and y is units digit

1. x is a factor of y. Lets assume x = 2,3 or 4 then y can have values 2,4,6,8,9 . All possible combinations will give a composite number . hence suff
2. we do not have any info about units digit so insuff
hence A

Answer is C. X can also be 1. 1 is factor of all the numbers.