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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 < 1 ? (1) x < 8/9 (2) y < 1/8

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

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

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.

option 1 doesn't provide enough info to conclude anything concrete. we can have all 15 terms equal to 4 or all 15 terms can be different. hence insuff option 2 says some any 3numbers is 12 is possible only when all terms are equal. Hence suff

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

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

OA and explanations to follow.

here option 1 and 2 alone cannot be sufficient as the other unknown (x or y) can have any value now we have values for x and y given as x <n 8/9 and y < 1/8 x < 8/9 < 0.8888..... so x < 888/1000 similarly y<1/8 < 0.125 so y<125/1000

lets consider x = 887/1000 and y = 124/1000 adding both we get x + y = 1013/1000 which is more than 1 .So is x+y<1 is NO

now lets consider x= 880/1000 and y = 110/1000 adding both we get x+y = 990/1000 which is less than 1 hence answer is YES for "is x+y<1" so both together are also insuff

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

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

OA and explanations to follow.

for q4 1. x^2 + y^2 > z^2 lets assume x= 10 , y=5 and z= 11 then 10^2 + 5^2 > 11^2 but 10^4 + 5^4 < 11^4

lets assume x=10,y=5 and z = 4 then 10^2 + 5^2 > 4^2 and also 10^4 + 5^4 > 4^4 hence a is insuff

2. x+y > z we can consider the above 2 examples and this also becomes insuff

even if we consider both together we can prove it to be insuff considering the same values as stated in the 2 assumptions

will go with E

for q5 we know the cost of ticket for an adult and child 1. we know the ratio but no info about either the number of children or adults present now 3/2 is ratio given. let the number of children be 3n then number of adults will be 2n (can get it from ratio 3/2) now avg cost = (number of children * price of 1child's ticket + number of adults * price of 1 adult's ticket) / (number of children + number of adults) = 3n*2 + 2n*5/ 3n + 5n and we get Avg Cost. hence A is suff 2. no info about number of children hence insuff

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.

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

OA and explanations to follow.

the tasks which Patrick needs to complete in exactly 1 hour are vacuum the floors, fold the laundry, and put away the dishes after the dishwasher completes its cycle

we know that Patrick has exactly 60mins before the guest arrive and dishwasher needs 55 more mins to complete the cycle so Patrick has 5 or less than 5mins to complete the task of putting away the dishes (as he cannot put the dishes before dishwasher completes the cycle)

1. we know about time taken to complete vacuuming and folding but we have no info about dishes. Patrick may take 1,2,3,4,5,6,7, or even more time to put away the dishes So insuff

2. from info we know Patrick takes 7mins and dishwasher will need 55 mins which totals to 62mins or 1hr 2mins. So irrespective of the time need to vacuum and fold Patrick will not be able to complete all the 3 tasks in 60mins. hence suff

6. Are some goats not cows? (1) All cows are lions (2) All lions are goats.

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

OA and explanations to follow.

not entirely sure of this 1. says about cows and lions but we need to find about goats and cows so Insuff 2. says about goats and lions and we need to find about goats and cows so insuff

now considering both we know all cows are lions and all lions are goats. but from 1 we can conclude that some lions are not cows and we know all lions are goats are so some goats are not cows.

Frankly I am not sure if the explanation is convincing.

(1). St.1 is sufficient. say n = 10a + b, then according to statement n = a*(10+q) because a is a factor of b. Therefore n cant be prime as a>2. St.2 is insufficient. With 2 as tens digit n could be a prime (23 or 29) or not; there's no way to confirm without info on units digit.

A is the ans.

(2). No info in the stem. St.1 is infufficient. The other 2 angles might be 90 deg as well; there's no way to tell. St.2 is insufficient. We cannot comment on the sum of these angles yet. Only after combining the info in both st. we know that the sum of the angles mentioned in st.2 is 180 deg (sum of all angles in quad is 360). Then we get one of the angles as 60.

C is the ans.

(3). Plain arithmetic. We obviously need both st. coz to get some info on each of the variables. Add the inequalities to get x + y < 73/72. Clearly, x+y could lie between 1 and 73/72, hence the statements are inconclusive even when combined.

E is the ans.

(4). To answer this, one would need, in addition to the given statements, an inequality purely in terms of z and xy. We cannot derive it from the given statements.

E is the ans.

(5). In order to calculate just the avergage, we don't need the exact no. of each of the tkt types sold. Just the ratio will do. You may verify this by assuming the no. of children's tkts sold as 3x and no. of adults tkts sold as 2x. You would realise that in the final expression of average, x disappears. Hence, St. 1 is sufficient. St. 2 is insufficient. It says nothing about the no. of children's tkts sold.

A is the ans.

(6). Obviously we need both sts. Draw a Venn diagram: Cows is the smallest circle. Lions is the bigger circle containing Cows circle. Goats is the biggest circle containing both Cows and Lions circles. Clearly some goats are not cows.

(7). St.1 is insufficient. This only tells us that he'll finish other chores within 55 mins. Altho imp piece of info, we need to know more. St.2 is sufficient by itself coz irrespective of him being able to finish other chores well in time to put away the dishes, he'll still fall short of 2 mins.

B is the ans.

(8). St.1 is clearly insufficient. You can create infinite lists of 15 nos. with sum as 60 (rem, there are no contrainsts on the numbers- they may be negative or fractions etc.)

Before considering any argument seriously for answering this question, it is useful to think in this direction : Is atleast one of the nos. in the list not equal to the others?

Now consider st.2. Lets assume atleast 1 no. is diff. Now we can see an immediate contradiction with st.2. Inclusion or exclusion of this particular no. in a set of 3 will cause the sums to be diff. Therefore our assumption was wrong. All nos. are equal. St.2 is sufficient.

6. Are some goats not cows? (1) All cows are lions (2) All lions are goats.

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

OA and explanations to follow.

not entirely sure of this 1. says about cows and lions but we need to find about goats and cows so Insuff 2. says about goats and lions and we need to find about goats and cows so insuff

now considering both we know all cows are lions and all lions are goats. but from 1 we can conclude that some lions are not cows and we know all lions are goats are so some goats are not cows.

Frankly I am not sure if the explanation is convincing.

Asterix answered with a BIG eeeeeeekkk!!!!

You are missing something answer is not correct.
_________________

(1). St.1 is sufficient. say n = 10a + b, then according to statement n = a*(10+q) because a is a factor of b. Therefore n cant be prime as a>2. St.2 is insufficient. With 2 as tens digit n could be a prime (23 or 29) or not; there's no way to confirm without info on units digit.

A is the ans.

(2). No info in the stem. St.1 is infufficient. The other 2 angles might be 90 deg as well; there's no way to tell. St.2 is insufficient. We cannot comment on the sum of these angles yet. Only after combining the info in both st. we know that the sum of the angles mentioned in st.2 is 180 deg (sum of all angles in quad is 360). Then we get one of the angles as 60.

C is the ans.

(3). Plain arithmetic. We obviously need both st. coz to get some info on each of the variables. Add the inequalities to get x + y < 73/72. Clearly, x+y could lie between 1 and 73/72, hence the statements are inconclusive even when combined.

E is the ans.

(4). To answer this, one would need, in addition to the given statements, an inequality purely in terms of z and xy. We cannot derive it from the given statements.

E is the ans.

(5). In order to calculate just the avergage, we don't need the exact no. of each of the tkt types sold. Just the ratio will do. You may verify this by assuming the no. of children's tkts sold as 3x and no. of adults tkts sold as 2x. You would realise that in the final expression of average, x disappears. Hence, St. 1 is sufficient. St. 2 is insufficient. It says nothing about the no. of children's tkts sold.

A is the ans.

(6). Obviously we need both sts. Draw a Venn diagram: Cows is the smallest circle. Lions is the bigger circle containing Cows circle. Goats is the biggest circle containing both Cows and Lions circles. Clearly some goats are not cows.

(7). St.1 is insufficient. This only tells us that he'll finish other chores within 55 mins. Altho imp piece of info, we need to know more. St.2 is sufficient by itself coz irrespective of him being able to finish other chores well in time to put away the dishes, he'll still fall short of 2 mins.

B is the ans.

(8). St.1 is clearly insufficient. You can create infinite lists of 15 nos. with sum as 60 (rem, there are no contrainsts on the numbers- they may be negative or fractions etc.)

Before considering any argument seriously for answering this question, it is useful to think in this direction : Is atleast one of the nos. in the list not equal to the others?

Now consider st.2. Lets assume atleast 1 no. is diff. Now we can see an immediate contradiction with st.2. Inclusion or exclusion of this particular no. in a set of 3 will cause the sums to be diff. Therefore our assumption was wrong. All nos. are equal. St.2 is sufficient.

B is the ans

Red part: answer is not correct.
_________________

#2 i picked E, as lets say if two angles are 90, with statement 2, we could have 90 90 45 135. or 90 90 60 120. so even with statement 1 and 2, it's inconclusive

#6 this one is tricky tho, because if we combine both statement, we have: all cows are lions, all lions are goats....so cows <= lions lions <= goats therefore cows <= goats, so it could be that all the goats are cows, or it could also be that there are extra goats that are NOT cows, so i thought this might also be inconclusive (could be E, but not sure if it was meant to be reasoned this way)...but might be a stretch.

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.

Given: \(n>20\) --> two digit integer can be written as follows: \(n=10b+a>20\) --> \(2\leq{b}\leq{9}\), \(0\leq{a}\leq{9}\).

(1) tells that \(a=kb\), (\(0\leq{k}\leq{4}\)) --> \(n=10b+a=10b+kb=b(10+k)\) --> as \(b\geq{2}\), \(n\) will always be composite and factor of \(b\). Sufficient

(2) tell that \(b=2\), but \(n\) can be for instance composite \(25\) or prime \(29\). Not sufficient.

Answer: A.

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.

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180(n-2), where n is # of sides) (1) Angles can be 90+90 + any combination of two angels totaling 180. Not sufficient. (2) <ABC=2<BCD. Not sufficient

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

Answer: E.

3. Is x + y < 1 ? (1) x < 8/9 (2) y < 1/8

(1) Info only about x. Not sufficient (2) Info only about y. Not sufficient (1)+(2) x+y<73/72 Not sufficient

Answer: E.

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

Plugging numbers from Pythagorean triplets is the best way to get that not sufficient.

Answer E.

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.

Av. cost=(2*C+5*A)/(C+A) (1) 3A=2C A=2C/3 --> Av.cost C(2+5*2/3)/C(1+2/3) --> (2+5*2/3)/(1+2/3) Sufficient (2) A=80 know nothing about C Not sufficient.

Answer: A

6. Are some goats not cows? (1) All cows are lions (2) All lions are goats.

This is good one: Question generally asks is g>c? (1) c<=l Not sufficient (2) l<=g Not sufficient (1)+(2) c<=l<=g --> If all cows are lions and all lions are goats there are no goat, which are not cows, in other case there are, so Not sufficient

Answer: E.

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.

(1) Don't know how much time is needed to put away dishes. Not sufficient (2) If dishwasher will stop after 55 min and 7 min is needed to put away dishes 55+7=62>60, so Patrick won't complete all of the tasks before his guests arrive in exactly 1 hour. Sufficient

Answer: B

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.

(1) S=60 list can contain numerous combination of 15 numbers totaling 60. Not sufficient. (2) If the sum of ANY 3 numbers=12 all numbers=12/3=4. Sufficient.

6. Are some goats not cows? (1) All cows are lions (2) All lions are goats.

This is good one: Question generally asks is g>c? (1) c<=l Not sufficient (2) l<=g Not sufficient (1)+(2) c<=l<=g --> If all cows are lions and all lions are goats there are no goat, which are not cows, in other case there are, so Not sufficient

Answer: E.

hiiii Bunuel...

for the above given question, is my way of answering right??

1) all cows are lions.-----this alone insuff 2) all lions are goats----- this alone insuff

now taking both 1&2 together, we can form a venn diagram, cows in the innermost circle, lions- a super set of cows and goats- a super set of lions.

now the question asks--"are some goats cows?," there are two sets of goats, a)goats that are cows, i.e., GnC (innermost circle region) and b) goats that are not cows GnC' (C' means C complement, region outside the innermost circle).. two answers are possible, hence insuff..

6. Are some goats not cows? (1) All cows are lions (2) All lions are goats.

This is good one: Question generally asks is g>c? (1) c<=l Not sufficient (2) l<=g Not sufficient (1)+(2) c<=l<=g --> If all cows are lions and all lions are goats there are no goat, which are not cows, in other case there are, so Not sufficient

Answer: E.

hiiii Bunuel...

for the above given question, is my way of answering right??

1) all cows are lions.-----this alone insuff 2) all lions are goats----- this alone insuff

now taking both 1&2 together, we can form a venn diagram, cows in the innermost circle, lions- a super set of cows and goats- a super set of lions.

now the question asks--"are some goats cows?," there are two sets of goats, a)goats that are cows, i.e., GnC (innermost circle region) and b) goats that are not cows GnC' (C' means C complement, region outside the innermost circle).. two answers are possible, hence insuff..

Answer: E

The question is: "are some goats not cows?"

If we use Venn diagram we can have two cases:

A. The inner circle (cows) is smaller than the biggest circle (goats), in this case we have goats which are not cows; B. Three circles are equal (which doe not violate the statements) which gives no goats which are not cows.

A. The inner circle (cows) is smaller than the biggest circle (goats), in this case we have goats which are not cows; B. Three circles are equal (which doe not violate the statements) which gives no goats which are not cows.

Two different answers. Not sufficient, E.

Hope it's clear.

clear as a crystal.. i didn't take into account the possibility of all three circles being equal... silly of me.. nice explanation Bunuel..thanx
_________________

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.

Answer should be C.

(1) Any two angles can be 90 degrees so Insuff. (2) No Information about angles DAB and CDA are gien so Insff.

Two adjecent angles can not be 90 otherwise the other two will also be 90 in which case either of ABC or BCD = 180 (not a corner but a straight line). This implies that either ABC or BCD has to be 90. Again ABC can not be 90 otherwise BCD = 2(ABC) = 180 (a straight line). S0 there is only one possible situation where BAD = BCD = 90, which implies ABC = 1/2 (BCD) = 45 and ADC = 360 - (90+90+45) = 135.

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