divelab/Sys2Bench huggingface dataset:
Question: If 8 men or 12 women can do a piece of work in 35 days, in how many days can the same work be done by 6 men and 11 women?
Options:
A)10 days
B)11 days
C)13 days
D)15 days
E)21 days
Rationale: 8men = 12women (i.e 2men = 3women)
12women 1 day work= 1/35
soln:
6men(9women)+ 11women=20women=?
1 women 1 day work =12*35= 1/420
so, 20 women work= 20/420=1/21
ans: 21 days
ANSWER:E
Answer: E
Question: P and Q are in a relay race. P runs the first leg of the course in 3 seconds. Q runs the second leg of the course in 57 seconds. What was the average time they took to run a leg of the course?
Options:
A)30
B)32
C)34
D)36
E)38
Rationale: (3 seconds +57 seconds)/2= 30 seconds
Correct option is: A
Answer: A
Question: Exactly 3/8 of the people in the room are under the age of 21, and exactly 5/12 of the people in the room are over the age of 65. If the total number of the people in the room is greater than 50 and less than 100, how many people in the room are under the age of 21?
Options:
A)21
B)36
C)39
D)60
E)65
Rationale: The total number of the people in the room must be a multiple of both 8 and 12 (in order 3/7 and 5/13 of the number to be an integer), thus the total number of the people must be a multiple of LCM of 8 and 12, which is 96.
Since, the total number of the people in the room is greater than 50 and less than 100, then there are 96 people in the room.
Therefore there are 3/8*96=36 people in the room under the age of 21.
Answer: B.
Answer: B
Question: What is the sum of the multiples of 4 between 38 and 127 inclusive?
Options:
A)1804
B)1816
C)1824
D)1828
E)1832
Rationale: the fastest way in an AP is to find the average and multiply with total integers..
between 38 and 127, the smallest multiple of 4 is 40 and largest =124..
average=(40+124)/2=164/2=82..
total numbers = (124-40)/4 + 1= =84/4+1=27+1=22..
sum=82*22=1804
ans A
Answer: A
Question: A fort had provision of food for 150 men for 45 days. After 10 days, 30 men left the fort. The number of days for which the remaining food will last, is:
Options:
A)29 1/5
B)37 1/4
C)43 3/4
D)54
E)48
Rationale: After 10 days : 150 men had food for 35 days.
Suppose 120 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 120 : 150 :: 35 : x <=> 120 x x = 150 x 35
=> x =150 x 35/120
=> x = 43 3/4.
Correct answer is C
Answer: C
Question: A train of 25 carriages, each of 60 meters length, when an engine also of 60 meters length is running at a speed of 60 kmph. In what time will the train cross a bridge 1.5 km long?
Options:
A)2 mins 14 sec
B)2 mins 34 sec
C)180 sec
D)4 mins 54 sec
E)2 mins 44 sec
Rationale: D = 25 * 60 + 1500 = 3000 m
T = 3000/60 * 18/5 = 180 sec
ANSWER:C
Answer: C
Question: If 4 men can paint 60 m long wall in 3 days, then 5 men can paint 50 m long wall in
Options:
A)3days
B)2days
C)5days
D)6days
E)1day
Rationale: The length of wall painted by one man in one day = 60 / 4 Ã— 3 = 5 m
No. of days required to paint 50 m wall by 5 men = 50/ 5 Ã— 5 = 2 day.
B
Answer: B
Question: if a tap could fill entire tank in 18 hrs due to leakage, then in how much time tank can be emptied by leakage if tap can fill entire tank in 12 hrs without leakage?
Options:
A)35 hrs
B)36 hrs
C)37 hrs
D)38 hrs
E)39 hrs
Rationale: if a tap could fill entire tank in 18 hrs due to leakage,
tap can fill entire tank in 12 hrs without leakage.
Tank emptied in 0ne hr by leakage = 1/12-1/18= (6-4)/72=2/72=1/36.
Full Tank can be emptied in 36 hrs.
ANSWER:B
Answer: B
Question: Two trains of equal lengths take 10 seconds and 15 seconds respectively to cross a telegraph post. If the length of each train be 120 metres, in what time (in seconds) will they cross each other travelling in opposite direction?
Options:
A)10
B)12
C)15
D)18
E)20
Rationale: Speed of the first train =120/10m/sec = 12 m/sec.
Speed of the second train =120/15m/sec = 8 m/sec.
Relative speed = (12 + 8) = 20 m/sec.
Required time =(120 + 120)/20sec = 12 sec. ANSWER:B
Answer: B
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 300 m long?
Options:
A)176 Sec
B)190 Sec
C)178 Sec
D)150 Sec
E)276 Sec
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1500 m
T = D/S
T = 1500/10
T = 150 Sec
Answer:D
Answer: D
Question: Find the L.C.M of 12, 25, 24 and 20.
Options:
A)240
B)600
C)320
D)150
E)250
Rationale: Explanation:
6 x 2 x 2 x 5 x 5 = 600
Answer: Option B
Answer: B
Question: There are 6 red balls,8 blue balls and 7 green balls in a bag. If 5 are drawn with replacement, what is the probability at least three are red?
Options:
A)312/16808
B)312/16807
C)312/16805
D)312/16838
E)312/16111
Rationale: At least 3 reds means we get either : 3 red or 4 red or 5 red. And this is a case of replacement.
case 1 : 3 red balls : 6/21 x 6/21 x 6/21 x 15/21 x 15/21
case 2 : 4 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 15/21
case 3 : 5 red balls : 6/21 x 6/21 x 6/21 x 6/21 x 6/21
Total probability = = (6/21 x 6/21 x 6/21 x 15/21 x 15/21)+(6/21 x 6/21 x 6/21 x 6/21 x (15 )/21)+ (6/21 x 6/21 x 6/21 x 6/21 x 6/21)
= 312/16807
Answer:B
Answer: B
Question: For her customer feedback score, Jess wants to average at or above an 8.0 rating. For the month of June, she received the following scores: 7, 6, 8, 7, 9, 10, 6, 6, 8 and 7. By what percent did she fall short of her goal?
Options:
A) 4%
B) 5%
C) 8%
D) 10%
E) 2.5%
Rationale: Expected minimum rating = 8
Deviation from the expected minimum rating = (-1 - 2 + 0 - 1 + 1 + 2 - 2 - 2 + 0 - 1)/10 = -2/10 = -0.2
Current rating is 0.2 less than 8.
Percentage = (0.2/8)*100 = 2.5%
Answer: E
Answer: E
Question: Contractor is engaged for 30days on the condition that he receives Rs.25 for eachday he works &isfined Rs.7.50 for each day is absent. He gets Rs.425 in all. For how many days was heabsent?
Options:
A)5
B)10
C)15
D)16
E)19
Rationale: 30 * 25 = 750
425
-----------
325
25 + 7.50 = 32.5
325/32.5 = 10
B
Answer: B
Question: At the store, Sam bought a shirt and a toaster. There was a 5% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax?
Options:
A)0.95(K – T)
B)0.95K – T
C)0.95(K – 1.05T)
D)(K – T)/1.05
E)(K/1.05) – T
Rationale: 1.05S + 1.05T = K
1.05S = K - 1.05T
S = (K/1.05) - T
The answer is E.
Answer: E
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
Options:
A)82
B)17
C)12
D)82
E)18
Rationale: Explanation:
T = 9/45 * 60 = 12
Answer: Option C
Answer: C
Question: From the beginning to the end of 2007, the price of a stock rose 20 percent. In 2008, it dropped 25 percent. In 2009, it rose 30 percent. What percent of the stockâ€™s 2007 starting price was the price of the stock at the end of 2009?
Options:
A)80
B)117
C)95
D)100
E)108
Rationale: Assume a value at the beginning of 2007. As this is a % question, assume P=100.
At the end of 2007 it becmae = 1.2*100=120
At the end of 2008 it decreased by 25% = 120*.75 = 90
At the end of 2009 it increased by 30% = 90*1.3 = 117
Thus ratio = 117/100 = 1.17 (in % terms = 117%). Thus B is the correct answer.
Answer: B
Question: 5 men and 12 boys finish a piece of work in 4 days, 7 men and 6 boys do it in 5 days. The ratio between the efficiencies of a man and boy is?
Options:
A)1:2
B)2:1
C)2:3
D)6:5
E)3:1
Rationale: Explanation:
5Men + 12Boys ----- 4 days
7Men + 6Boys ------- 5 days
20Men + 48Boys = 35Men + 30Boys
18Boys = 15Men => 5Men = 6Boys
Men : Boys = 6:5
Answer: D
Answer: D
Question: A reduction of 30% in the price of apples would enable a man to obtain 54 more for Rs.30, what is reduced price per dozen?
Options:
A)1
B)2
C)6
D)7
E)10
Rationale: B
30*(30/100) = 9 --- 54
? --- 12 => Rs.2
Answer: B
Question: Rain is falling at a rate of 36 centimeters per hour all over Springfield. Somewhere downtown in Springfield a group of old people is waiting for the rain to stop. If the rain filled a round tank the with a base area of 150 square centimeters and a depth of 6 centimeters, how long did the people wait for the rain to stop?
Options:
A)6 hours
B)7 hours 15 minutes
C)5 hours
D)12 hours
E)10 hours
Rationale: Answer is : A, 6 hours
The volume of the tank is irrelevant and only height matters since rain fell all over the city.
Thus, it takes only 36 / 6 = 6 hours of rain to fill the tank
Answer: A
Question: A boat can move upstream at 34 kmph and downstream at 30 kmph, then the speed of the current is?
Options:
A)2
B)9
C)5
D)9
E)5
Rationale: US = 34
DS = 30
M = (34 - 30)/2 = 2
Answer: A
Answer: A
Question: Of 58 players on a cricket team, 37 are throwers. The rest of the team is divided so one third are left- handed and the rest are right handed. Assuming that all throwers are right handed, how many right- handed players are there total?
Options:
A)51
B)55
C)59
D)71
E)92
Rationale: Total = 58
Thrower = 37
Rest = 58 - 37 = 21
Left Handed = 21/3 = 7
Right handed = 14
If all Thrower are right handed then total right handed is 37 + 14 = 51
so A. 51 is the right answer
Answer: A
Question: If Rs. 544 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively?
Options:
A)s.300
B)s.360
C)s.389
D)s.384
E)s.323
Rationale: (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A;s share = 544 * 2/17 = Rs. 64
B's share = 544 * 3/17 = Rs. 96
C's share = 544 * 12/17 =Rs.384.
Answer:D
Answer: D
Question: From a total of 5 boys and 3 girls, how many 4-person committees can be selected if the committee must have exactly 2 boys and 2 girls?
Options:
A)16
B)24
C)30
D)120
E)240
Rationale: Answer=C=30
No of 4 person committees that can be formed=5C2*3C2=30
Answer C
Answer: C
Question: Sandy can do a job in 18 days and Molly can do the same job in 36 days. If they work together, in how many days will they complete the job?
Options:
A)6
B)8
C)10
D)12
E)15
Rationale: Sandy can do 1/18 of the job each day.
Molly can do 1/36 of the job each day.
The combined rate is 1/18 + 1/36 = 1/12 of the job each day.
The job will take 12 days.
The answer is D.
Answer: D
Question: The cricket team of 11members is 29yrs old & the wicket keeper is 3 yrs older. If the ages ofthese 2are excluded, the average age of theremaining players is 1 year less than the average age of the whole team. What is the average age of the team ?
Options:
A)21
B)22
C)23
D)26
E)28
Rationale: Let the average age of the whole team be x years.
11x - (29 + 32) = 9 (x - 1)
=> 11x - 9x = 52
=> 2x = 52
=> x = 26.
So, average age of the team is 26 years.
D
Answer: D
Question: A man can row at 5 kmph in still water .If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back ,how far is the place ?
Options:
A)2.4 km
B)2.5 km
C)3 km
D)3.6 km
E)None of these
Rationale: Answer A
Solution
Speed downstream = kmph = 6 kmph,Speed upstream = (5 - 1)
kmph = 4 kmph.
Let the required distance be x km.
Then,x/6 + x/4 = 1 => 2x + 3x = 12 5x = 12=> x = 2.4 km. Answer A
Answer: A
Question: he average marks of a class of 30 students is 40 and that of another class of 50 students is 60. Find the average marks of all the students?
Options:
A)52.2
B)59.5
C)52.8
D)52.5
E)52.1
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 60 = 3000
Sum of the marks for the class of 80 students =
1200 + 3000 = 4200
Average marks of all the students = 4200/80
= 52.5
Answer:D
Answer: D
Question: A certain bakery baked a batch of 400 cookies one day. Of those, 320 contained nuts, 230 contained chocolate chips, and 85 contained neither nuts nor chocolate chips. What is the fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch?
Options:
A)13
B)27
C)41
D)43
E)51
Rationale: Cookies which have both nuts and chocolate chips = 235
Let fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that
batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch = x
(235+x)/(400+x) = 6/10
=>2350 + 10x = 2400 + 6x
=> 4x = 50
=> x = 12.5
Therefore x = 13
Answer A
Answer: A
Question: A certain car uses one gallon of gasoline every 38 miles when it travels on highway, and one gallon of gasoline every 20 miles when it travels in the city. When a car travels 4 miles on highway and 4 additional miles in the city, it uses what percent more gasoline than if it travels 8 miles on the highway?
Options:
A)15%
B)20%
C)22.5%
D)45%
E)50%
Rationale: 4 miles on the highway = 4/38 gallons;
4 miles in the city = 4/20 gallons;
Total = 4/38 + 4/20 = 29/95 gallons.
8 miles on the highway = 8/38 gallons .
The % change = (29/95 - 8/38)/(8/38) = 0.45.
Answer: D.
Answer: D
Question: Victor's job requires him to complete a series of identical jobs. If Victor is supervised at work, he finishes each job three days faster than if he is unsupervised. If Victor works for 144 days and is supervised for half the time, he will finish a total of 36 jobs. How long Q would it take Victor to complete 10 jobs without any supervision?
Options:
A)34
B)52
C)60
D)70
E)92
Rationale: Rate when supervised = (job)/(time) = 1/t.
Rate when unsupervised = (job)/(time) = 1/(t+3).
For 144/2=72 days he is supervised and for 144/2=72 days he is unsupervised and does 36 jobs:
72/t + 72/(t+3) = 36 --> t=3 days --> t+3 = 6 days.
Victor to complete 10 jobs without any supervision will need Q 10(t + 3) = 60 days.
Answer: C.
Answer: C
Question: Each child has 6 crayons and 12 apples. If there are 12 children, how many crayons are there in total?
Options:
A)22
B)65
C)72
D)78
E)90
Rationale: 6*12=72.Answer is C
Answer: C
Question: If a town of 25,000 people is growing at a rate of approx. 1% per year, the population of the town in 5 years will be closest to?
Options:
A)26000
B)27000
C)28000
D)29000
E)30000
Rationale: Let population in the beginning = 100
at the end of 1st year population = 100+1% of 100 = 100+1 = 101
at the end of 2nd year population = 101+1% of 101 = 101+1 approx = 102 approx (on the lower side because 1% of 101 is greater than 1)
at the end of 3rd year population = 102+1% of 102 = 102+1 approx = 103 approx (on the lower side because 1% of 102 is greater than 1)
at the end of 4th year population = 103+1% of 103 = 103+1 approx = 104 approx (on the lower side because 1% of 103 is greater than 1)
at the end of 5th year population = 104+1% of 104 = 104+1 approx = 105 approx (on the lower side because 1% of 104 is greater than 1)
i.e. 5% greater than 25000 = 25000+5% of 25000 = 25000+1250 = 26250 (on the lower side)
i.e. Population must be greater than 26250 but since the closest option is 26000 so
Answer: option A
Answer: A
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is :
Options:
A)11
B)18
C)19
D)287
E)27
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1 = 57 years.
Required average = (57/3) = 19 years.
Answer: C) 19
Answer: C
Question: If x and y are prime numbers such that x > y > 5, then x^2 − y^2 must be divisible by which one of the following numbers?
Options:
A) 3
B) 7
C) 5
D) 9
E) 12
Rationale: If x=7 and y=5, then x^2-y^2=24 and 24 is divisible only by 12 from the options, thus it must be correct.
Answer: E.
Answer: E
Question: X can run a kilometer race in 4 1/2 min while Y can run same race in 5 min. How many meters start can X give Y in a kilometer race, so that the race mat end in a dead heat?
Options:
A)50 m
B)200 m
C)150 m
D)100 m
E)250 m
Rationale: D
100 m
X can give Y (5 min - 4 1/2 min) = 30 sec start.
The distance covered by Y in 5 min = 1000 m.
Distance covered in 30 sec = (1000 * 30)/300 = 100 m.
X can give Y 100m start.
Answer: D
Question: A boy has Seven trousers and 14 shirts. In how many different ways can he select a trouser and a shirt?
Options:
A)38 ways
B)87 ways
C)66 ways
D)98 ways
E)121 ways
Rationale: Explanation:
The boy can select one trouser in seven ways.
The boy can select one shirt in 14 ways.
The number of ways in which he can select one trouser and one shirt is 7 * 14 = 98 ways.
Answer: D
Answer: D
Question: A canoe has two oars, left and right. Each oar either works or breaks. The failure or non-failure of each oar is independent of the failure or non-failure of the other. You can still row the canoe with one oar. The probability that the left oar works is 3/5. The probability that the right oar works is also 3/5. What is the probability Q that you can still row the canoe?
Options:
A)9/25
B)10/25
C)6/10
D)2/3
E)21/25
Rationale: Simply look at the question from the other side. What is the probability that you can’t row the canoe? This would be 2/5 x 2/5 = 4/25.
Using the idea that the probability Q of something happening is 1 – the probability that it doesn’t happen, you can use the following equation to reach the right answer: 1 – 4/25 = 21/25.Answer choice E.
Answer: E
Question: On a certain date, Pat invested $10,000 at x percent annual interest, compounded annually. If the total value of the investment plus interest at the end of 12 years will be $40,000, in how many years, the total value of the investment plus interest will increase to $120,000?
Options:
A)15
B)21
C)18
D)20
E)24
Rationale: if i were to choose during the test, would go for 18 or 20. probably 18 cuz it wont take too long to get the value doubled....
I found a method: Rule of 72.
Given an x% return, it takes 10,000 to quadralope 12 years.
So according to the rule: 72/x is the no of years 10,000.00 took to double 20,000.00.
Again, 20,000.00 took to double 40,000.00 same (72/x) no of years.
72/x+ 72/x = 12
x = 12% (though rate here is not very much required).
Again, 40,000.00 takes the same (72/x) no of years to double 120,000.00.
72/x = 6 years.
So altogather:
10,000 - 20,000 = 6 years
20,000 - 40,000 = 6 years
40,000 - 80,000 = 6 years
80,000 - 120,000 = 3 years
total 21 years.
Answer B
Answer: B
Question: The compound ratio of 3:4, 3:2 and 4:5?
Options:
A)1:9
B)1:7
C)1:2
D)9:10
E)1:4
Rationale: 3/4 * 3/2 * 4/5
= 9/10
=9:10
Answer: D
Answer: D
Question: Ann and Bob drive separately to a meeting. Ann's average driving speed is greater than Bob's avergae driving speed by one-third of Bob's average driving speed, and Ann drives twice as many miles as Bob. What is the ratio R of the number of hours Ann spends driving to the meeting to the number of hours Bob spends driving to the meeting?
Options:
A)8:3
B)3:2
C)4:3
D)2:3
E)3:8
Rationale: Say the rate of Bob is 3mph and he covers 6 miles then he needs 6/3=2 hours to do that.
Now, in this case the rate of Ann would be 3+3*1/3=4mph and the distance she covers would be 6*2=12 miles, so she needs 12/4=3 hours for that.
The ratio R of Ann's time to Bob's time is 3:2.
Answer: B.
Answer: B
Question: A vessel of capacity 2 litre has 25% of alcohol and another vessel of capacity 6 litre had 40% alcohol. The total liquid of 8 litre was poured out in a vessel of capacity 10 litre and thus the rest part of the vessel was filled with the water. What is the new concentration of Mixture?
Options:
A)31%.
B)71%.
C)49%.
D)29%.
E)51%.
Rationale: 25% of 2 litres = 0.5 litres
40% of 6 litres = 2.4 litres
Therefore, total quantity of alcohol is 2.9 litres.
This mixture is in a 10 litre vessel. Hence, the concentration of alcohol in this 10 litre vessel is 29%
ANSWER:D
Answer: D
Question: A pipe can fill a cistern in 18 minutes whereas the cistern when fill can be emptied by a leak in 36 minutes. When both pipes are opened, find when the cistern will be full?
Options:
A)17
B)36
C)70
D)13
E)12
Rationale: 1/18 - 1/36 = 1/36
36 minutes
Answer: B
Answer: B
Question: The area of one square is x^2 + 8x + 16 and the area of another square is 4x^2 − 12x + 9. If the sum of the perimeters of both squares is 32, what is the value of x?
Options:
A)0
B)2
C)2.5
D)7/3
E)10
Rationale: spotting the pattern of equations both are in form of (X+C)^2 so
A1= (x+4)^2A2= (2x-3)^2
L1= x+5L2= 2x-3
P1 = 4( x+4)P2=4(2x-3)
P1+P2=32
4( x+4) +4(2x-3)=32..............> X=7/3
Answer: D
Answer: D
Question: In a two-digit number, the digit in the unit’s place is four times the digit in ten’s place and sum of the digits is equal to 10. What is the number?
Options:
A)14
B)41
C)41
D)None of these
E)Cannot be determined
Rationale: Solution
Let the ten's digits be x. Then, unit's digit = 4x.
∴ x + 4x = 10 ⇔ 5x = 10 ⇔ x = 2.
So, ten's digit = 2, unit's digit = 8.
Hence, the required number is 28.
Answer D
Answer: D
Question: If p and q are integers, such that p < 4 < q, and s is a nonnegative integer, which of the following must be true?
Options:
A)p^2 < q^2
B)p + q = 0
C)sp < sq
D)sp ≠ sq
E)p/q < s
Rationale: We're told that P < 0 < Q and that S is a NON-NEGATIVE INTEGER. We're asked which of the following MUST be true.
P = -2
Q = 5
S = 0
Answer A: P^2 < Q^2.... 4 < 1 NOT TRUE
Answer B: P+Q=0... -2+1 = -1 NOT TRUE
Answer C: SP < SQ... 0 < 0 NOT TRUE
Answer D: SP ≠ SQ... This is TRUE
Answer E: P/Q < S... not TRUE
D
Answer: D
Question: For any integer n greater than 1, #n denotes the product of all the integers from 1 to n, inclusive. How many prime numbers W are there between #6 +2 and #6 +6 , inclusive?
Options:
A)None
B)One
C)Two
D)Three
E)Four
Rationale: None is the answer. A.
Because for every k 6! + k :: k, because 6! :: k, since k is between 2 and 6.A
Answer: A
Question: If (18^a) * 9^(3a – 1)= (2^7)(3^b) and a and b are positive integers, what is the value of a?
Options:
A)22
B)11
C)9
D)6
E)7
Rationale: (18^a) * 9^(3a – 1)= (2^7)(3^b)
= 2^a . 9^a . 9^(3a – 1) = (2^7)(3^b)
Just compare powers of 2 from both sides
Answer = 7 = E
Answer: E
Question: If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
II. ab < 1
III.a/b > 1
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I and III only
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (D).
Answer: D
Question: If a radio is purchased for Rs 490 and sold for Rs 465.50
Find the loss%?
Options:
A)5%
B)4%
C)6%
D)8%
E)7%
Rationale: C.P=Rs 490 S.P=Rs 465.50
Loss=C.P-S.P=490-465.50=Rs 24.50
Loss%=(loss*100)/C.P%
=(24.50*100)/490%=5%
ANSWER A 5%
Answer: A
Question: An isosceles triangle those sides are 13cm,13cm,10cm long inscribed in a circle.find the radius of the circle
Options:
A)8 cm
B)9 cm
C)10 cm
D)11 cm
E)7 cm
Rationale: a,b,c are sides of triangle ,ad is the median, ad^2=ab^2-bd^2 then ad=12,the centriod median divides into 2:1 ratio so 12 will be divide into 2:1 ratio so 8 is radius.
so ans is 8 cm
ANSWER:A
Answer: A
Question: Two identical circles intersect such that their centers and the points at which they intersect form a square of side 4 cm. What is the area of the region where the two circles intersect?
Options:
A)16 - 4pi
B)4 - pi
C)2pi - 4
D)8pi - 16
E)pi^2 - 4
Rationale: Drawing a diagram, we see that the radius of the circle equals the side of the square.
The area of intersection is: pi*r^2/4 - (r^2-pi*r^2/4) = pi*r^2/2 - r^2 = 8pi - 16
The answer is D.
Answer: D