divelab/Sys2Bench huggingface dataset:
Question: After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article?
Options:
A)226
B)255
C)1200
D)2771
E)332
Rationale: CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer:C
Answer: C
Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability E that the team will have exactly 2 women?
Options:
A)1/14
B)1/7
C)2/7
D)3/7
E)1/2
Rationale: 5C2 * 3C2 -> it gives combination of exactly 2 women and 2 men.
8C4 -> gives total possibilities of 4 people from 5 women and 3 men.
Probability = 5C2*3C2 / 8C4 = 3/7
SECOND METHOD:
Probability of two women -> 5/8 * 4/7.
probability of two men -> 3/6 * 2/5.
Probability: (5/8 * 4/7) * (3/6 * 2/5) = 1/14.
Answer: D
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
Options:
A)110 km/hr
B)80 km/hr
C)60 km/hr
D)50 km/hr
E)120 km/hr
Rationale: Answer: Option C
Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5 = 60 km/hr.
Answer: C
Question: An urn contains 10 balls, numbered from 1 to 10. If 2 balls are selected at random with replacement from the urn, what is the probability B that the sum of the 2 numbers on the balls will be even?
Options:
A)25%
B)37.5%
C)50%
D)62.5%
E)75%
Rationale: Correct Answer: C
Since there are 5 even numbered balls and 5 odd numbered balls, the probability B of selecting either an even or an odd is 5/10= 1/2. In order for the sum of the numbers on the two balls to be even, either both numbers must be even or both numbers must be odd; one even and one odd number would add to an odd number. The probability of selecting two even numbers is:
1/2 * 1/2= 1/4
The probability of selecting two odd numbers is also:
1/2 * 1/2= 1/4
Adding both probabilities gives 1/4+1/4= 1/2 , or 50%, as the probability that the sum of the numbers will be even. Thus, the correct answer is (C).
Answer: C
Question: If a car went the first third of the distance at 80 kmh, the second third at 24 kmh, and the last third at 30 kmh, what was the average speed of the car for the entire trip?
Options:
A)36 kmh
B)40 kmh
C)42 kmh
D)44 kmh
E)34 kmh
Rationale: Assume D/3 = 240 (this number is convenient because it is divisible by 80, 24 and 30)
So:
240 = 80*T1 = 3 hrs
240 = 24*T2 = 10 hrs
240 = 30*T3 = 8 hrs
T = T1 + T2 + T3 = 21 hrs
D = RT
(240*3) = R*21
R = 34
ANSWER: E
Answer: E
Question: What is the rate percent when the simple interest on Rs.900 amount to Rs.160 in 4 Years?
Options:
A)4.44
B)5.44
C)6.44
D)7.44
E)8.44
Rationale: 160 = (900*4*R)/100
R = 4.44%
Answer: A
Answer: A
Question: When a number is divided by 4 &then multiply by 12 the answer is 9 what is the no.?
Options:
A)3
B)5
C)5.6
D)5.7
E)6.5
Rationale: if $x$ is the number, x/4 * 12 = 9
=> 3x = 9
=> x = 3
A
Answer: A
Question: Last year, the price of a vacation package was P. At the beginning of this year, the price went up 50%. Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price. In terms of P, how much did Lucas pay?
Options:
A) P + 10
B) 1.1*P
C) 0.50*P
D) 0.05*P
E) 1.05*P
Rationale: Last year price = P;
This year price = 1.5P;
Lucas used a travel voucher to purchase the vacation package at 30% off this year’s price, thus he paid (1 - 0.3)*1.5P = 0.98P.
Answer: E.
Answer: E
Question: A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.75 less, he could have gained 25%. What is the cost price?
Options:
A)250
B)276
C)976
D)267
E)287
Rationale: CP1 = 100 SP1 = 90
CP2 = 80 SP2 = 80 * (140/100) = 112
22 ----- 100
55 ----- ? => Rs.250
Answer:A
Answer: A
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old id the mother at present?
Options:
A)46
B)49
C)40
D)21
E)19
Rationale: Let the mother's present age be x years. Then, the person's present age = 2/5 x years.
(2/5 x + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) => x = 40
Answer:C
Answer: C
Question: Speed of a boat in standing water is 14 kmph and the speed of the stream is 1.2 kmph. A man rows to a place at a distance of 4864 km and comes back to the starting point. The total time taken by him is:
Options:
A)700
B)200
C)540
D)120
E)635
Rationale: Explanation:
Speed downstream =(14+1.2)=15.2 kmph
Speed upstream =(14-1.2)=12.8 kmph
Total time taken=4864/15.2+4864/12.8=320+380=700 hours.
Answer:A
Answer: A
Question: There is enough provisions for 1200 girls in a hostel for 50 days. If there were 600 girls less, how long will the provision last?
Options:
A)75
B)80
C)90
D)95
E)100
Rationale: We have, M1D1 = M2D2
1200*50= 600* D2
D2 = 1200*50/600 = 100 days.
ANSWER:E
Answer: E
Question: At 1:00, Annie starts to bicycle along a 87 mile road at a constant speed of 15 miles per hour. Thirty minutes earlier, Scott started bicycling towards Annie on the same road at a constant speed of 12 miles per hour. At what time will they meet?
Options:
A)2:30
B)3:00
C)4:00
D)6:00
E)9:00
Rationale: In the first 30 minutes, Scott can travel 6 miles, so there are 81 miles left.
Together Annie and Scott can complete 27 miles.
81/27 = 3, so they will meet 3 hours after 1:00.
The answer is C.
Answer: C
Question: The sum of 5 consecutive even numbers of set x is 440. Find the sum of a different set of five consecutive integers whose second least number is 121 less than double the least number of set x?
Options:
A)220
B)230
C)235
D)236
E)240
Rationale: Let the five consecutive even numbers be 2(x - 2), 2(x - 1), 2x, 2(x + 1) and 2(x + 2)
Their sum = 10x = 440
x = 44 => 2(x - 2) = 84
Second least number of the other set = 2(84) - 121 = 47
This set has its least number as 46.
Sum of the numbers of this set = 46 + 47 + 48 + 49 + 50
= 48 - 2 + 48 - 1 + 48 + 48 + 1 + 48 + 2 => 5(48) = 240
E
Answer: E
Question: A certain sum of money is invested for one year at a certain rate of simple interest. If the rate of interest is 3% higher, then the invest earned will be 25% more than the interest earned earlier. What is the earlier rate of interest?
Options:
A)16
B)18
C)28
D)12
E)26
Rationale: If the interest earned is 25% more than the earlier interest then the rate of interest also should be 25% higher than the earlier rate.
Let the earlier rate of interest be x%.
Now it will be (x + 3)%
% increase = (x + 3) - x/x * 100
= 25
=> x = 12
Answer: D
Answer: D
Question: A person travels from P to Q a speed of 40 km/hr and returns by increasing his speed by 50%. What is his average speed for both the trips?
Options:
A)27
B)87
C)48
D)77
E)51
Rationale: Speed on return trip = 150% of 40 = 60 km/hr.
Average speed = (2 * 40 * 60)/(40 + 60) = 48 km/hr.
Answer: C
Answer: C
Question: There are four different models that are to appear in a fashion show. Two are from Europe, two are from South America, and two are from North America. If all the models from the same continent are to stand next to each other, how many ways can the fashion show organizer arrange the models?
Options:
A)192
B)48
C)64
D)24
E)8
Rationale: Since we have 3 continental pairs (EU, SA, NA), these 3 pairs have 4*3*2*1 = 24 Combinations. Within each pair, you have however 2 different ways to put them together for each of the pair (2*2*2 = 8). So we have 24*8 = 192.
Please correct me if im wrong.
Answer A.
Answer: A
Question: 30 men can do a work in 40 days. When should 16 men leave the work so that the entire work is completed in 40 days after they leave the work?
Options:
A)87 days
B)14 days
C)55 days
D)44 days
E)22 days
Rationale: Total work to be done = 30 * 40 = 1200
Let 16 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (16 * 40) = 1200
40P = 560 => P = 14 days
Answer:B
Answer: B
Question: 14 men can complete a piece of work in 30 days. In how many days can 24 men complete that piece of work?
Options:
A)17 1/2 days
B)26 3/4 days
C)22 1/2 days
D)29 days
E)20 days
Rationale: A
17 1/2 days
14 * 30 = 25 * x => x = 17 1/2 days
Answer: A
Question: The radius of a circular wheel is 1.75 m, how many revolutions will it make in traveling 1 km?
Options:
A)1000
B)2788
C)2677
D)2899
E)2771
Rationale: 2 * 22/7 * 1.75 * x = 11000
x = 1000
Answer: A
Answer: A
Question: A manufacturer produces a certain men's athletic shoe in integer sizes from 8 to 17. For this particular shoe, each unit increase in size corresponds to a 1/4-inch increase in the length of the shoe. If the largest size of this shoe is 30% longer than the smallest size, how long, in inches, is the shoe in size 15?
Options:
A)9.25
B)11.75
C)13.25
D)15.75
E)17.25
Rationale: Let x be the length of the size 8 shoe.
Then 0.3x = 9/4
x = 90/12 = 15/2 inches
The size 15 shoe has a length of 15/2 + 7/4 = 37/4 = 9.25 inches
The answer is A.
Answer: A
Question: In a room filled with 7 people, 4 people have exactly 1 sibling in the room and 3 people have exactly 3 siblings in the room. If two individuals are selected from the room at random, what is the probability that those two individuals are NOT siblings?
Options:
A)5/21
B)3/7
C)4/7
D)5/7
E)32/35
Rationale: There are suppose A B C D E F G members in the room 4 people who have exactly one sibling....A B C D....(A is Bs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDs∘SSsibl∈g∘SSand∘SSviceversa)∘SS(C∘SSis∘SSDssibl∈gandviceversa)(CisDs sibling and viceversa) (C is Ds sibling and viceversa)...now remaning EFG are 3 people who have exactly 3 siblings....(E has F and G as his/her sibling and so on..)
there are now 3 different set of siblings (A and B)
(C and D);(EFG)
Now first selecting 3 people out of 7 is 7C3=35
first sibling pair----(A and B)--selecting 3 people --3C3=1
second sibling pair (C and D)--selecting 3 people--3C3=1
third sibling pair (E F G)--selecting 3 out of 3 --3C3=1
total= 1+1+1=3
but,a/c to formula P(success)-1-p(fail)
here,p(failure)is selecting 3 people who are siblings
=3/35(35 is 7C3)
=1-3/35
=32/35
ANS E
Answer: E
Question: Joe is painting a rectangular room whose dimensions are given by a, b and c meters. Joe takes 4 hours to paint a wall with dimensions a and c. He takes 2 hours to paint a wall with dimensions b and c and 6 hours to paint the ceiling with dimensions a and b. If Joe works at a constant rate and a = 3, then what is the volume of the room?
Options:
A)4.5 cubic meters
B)2.4 cubic meters
C)3.0 cubic meters
D)3.6 cubic meters
E)It can’t be determined.
Rationale: Time to paint each wall as given in problem:
AC = 4 hours
BC = 2 hours
AB = 6 hours
Since he works at constant rate and it takes him twice as long to paint AC compared to BC
AC=2BC
Plug in 6 for A and you find that B=1.5 Since painting AB takes 3 times as long compared to BC,
AB=3BC
Plug in 6 for A and 3 for B and you find that C=1
A*B*C=3*1.5*1=4.5 cubic meters
Answer: A
Answer: A
Question: If ABC us a three digit number such that no one number is similar to other than how many possible values of ( a + 4b + c ) will be divisible by 40 :
Options:
A)18
B)16
C)15
D)12
E)11
Rationale: a b c
4 9 0 *1 because if 0 comes in first it is not a three digit number
1 9 3 *2
1 8 7 *2
2 8 6 *2
3 8 5 *2
3 7 9 *2
4 7 8 *2
7 6 9 *2
15
ANSWER:C
Answer: C
Question: The sector of a circle has radius of 24 cm and central angle 135o. Find its perimeter?
Options:
A)91.5 cm
B)11.5 cm
C)104.6 cm
D)92.5 cm
E)99.5 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 24) + 2(24)
= 56.6 + 48
= 104.6 cm
Answer:C
Answer: C
Question: If X=27^324 and Y=3^134, what is the units digit of X/Y?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: Basically it tests pattern : (3,9,7,1)
If we take write 27 in terms of 3 and take the dr to the top, it will result in 3^838
since pattern = 4 divide 838/4 and reminder = 2 ------- this points to 9 in the pattern (3,9,7,1)
ANSWER:E
Answer: E
Question: Find the number of square tiles to cover the floor of a room measuring 4.5 m * 10 m leaving 0.60 m space around the room. A side of square tile is given to be 11 cms?
Options:
A)2710
B)4764
C)2772
D)4000
E)2400
Rationale: 3.30 *8.80 = 11/100 * 11/100 * x => x = 2400
Answer: E
Answer: E
Question: Find the HCF of
23,46,827
Options:
A)227
B)83
C)23
D)827
E)None of these
Rationale: Answer: Option A
Explanation:
Whenever we have to solve this sort of question, remember the formula.
HCF =
HCF of Numerators LCM of Denominators
So answers will be option 1
Answer: Option A
Answer: A
Question: A certain school principal must choose 6 students to attend a field trip out of a group of 10 students. In addition, out of the 6 chosen students, the principal must select a note-taker and a treasurer. How many different ways are there for the principal to select the 6 students and then select the treasurer and the note-taker?
Options:
A)1,260
B)2,520
C)5,040
D)6,300
E)10,080
Rationale: 5 students can be selected out of 10 students in 10C6 ways.
out of the remaining 6 students,Note taker can be chosen in 6 ways.
Finally only 5 students remain from which we can choose a treasurer in 5 ways.
Total number of ways = 210 * 6 *5 = 6300
correct answer - D
Answer: D
Question: City A to city B, Andrew drove for 1hr at 42 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
Options:
A)55.5
B)57.5
C)61
D)61.5
E)62.5
Rationale: The total distance is 1×42+3×60=222
And the total time is 4 hours. Hence,
Average Speed=(Total Distance/Total Time)
=222/4=55.5
A
Answer: A
Question: A password of a computer consists of five digits 1 through 6. What is the probability that all digits are divisible by 3 ?
Options:
A)1/3
B)1/6
C)1/27
D)1/243
E)1/486
Rationale: For each digit there are six possibilities. Two of them (3 and 6) are divisible by three, so there is a one in three chance for each digit, and since the digits are independent of each other, overall probability is 1 / 3^5 or D
Answer: D
Question: 2/x + 3x = 3(x+2)
Options:
A)-9
B)1/3
C)-1/9
D)1/9
E)9
Rationale: We can solve - expand the right side, multiply by x on both sides and then subtract away the 3x^2 terms:
(2/X) + 3x = 3(x+2)
(2/x) + 3x = 3x + 6
2 + 3x^2 = 3x^2 + 6x
2 = 6x
1/3 = x
and to confirm, you can plug that answer back into the original equation to see that it makes the left and right sides equal.
B
Answer: B
Question: The average age of a class of 32 students is 16 yrs. if the teacher's age is also included, the average increases by one year. Find the age of the teacher
Options:
A)29 Years
B)32 Years
C)37 Years
D)49 Years
E)50 Years
Rationale: Total age of students is 32X16 = 512 Years
Total age inclusive of teacher = 33X (16+1) = 561
So, Teacher's age is 561-512 = 49 Yrs
There is a shortcut for these type of problems
Teacher's age is 16+(33X1) = 49 Years
D
Answer: D
Question: A bag contains 10 wool scarves, exactly one of which is red and exactly one of which is green. If Deborah reaches in and draws three scarves, simultaneously and at random, what is the probability that she selects the red scarf but not the green scarf?
Options:
A)3/11
B)5/23
C)7/30
D)9/37
E)11/48
Rationale: Total possible ways to choose three scarves is 10C3 = 120
We need to choose the red scarf and two of 8 other scarves (not the green scarf).
The number of successful possibilities is 8C2 = 28
P(red scarf but not green scarf) = 28/120 = 7/30
The answer is C.
Answer: C
Question: The water level in a rectangular swimming pool measuring 60 feet by 20 feet is to be lowered by 6 inches. How many gallons of water must be removed? (1 cu ft = 7.5 gallons)
Options:
A)100
B)250
C)4500
D)1200
E)5625
Rationale: 6 inches = 1/2 feet (there are 12 inches in a foot.), so 60*20*1/2=600 feet^3 of water must be removed, which equals to 600*7.5=4500 gallons.
Answer: C.
Answer: C
Question: On dividing a certain number by 342, we get 47 as remainder. if same number is divided by 18 . what will be the remainder?
Options:
A)7*9k+86
B)7*9k+56
C)8*4k+56
D)18*19K+47
E)19*6k+9
Rationale: number =324k+47
=(18*19k)+(18*2)+11
= 18*(19k+2)+11
= 18*19K+47
Answer(D)
Answer: D
Question: What is the probability that Carol and Bernie will get selected for a job they both applied for in a company, given that their chances of getting selected is 4/5 and 3/5 respectively?
Options:
A)8/25
B)11/24
C)12/25
D)12/25
E)12/23
Rationale: Explanation:
P(Carol) = 4/5
P(Bernie) = 3/5
E = {Carol and Bernie both get selected}
P(E) = P(Carol)*P(Bernie)
= 4/5 * 3/5
= 12/25
ANSWER: D
Answer: D
Question: A train which has 390 m long, is running 45 kmph. In what time will it cross a person moving at 9 kmph in same direction ?
Options:
A)26 sec
B)39 sec
C)36 sec
D)29 sec
E)30 sec
Rationale: Time taken to cross a moving person = length of train/ relative speed
Time taken = 390/((45-9) (5/18) = 390/ 36*(5/18) = 390/10 = 39 sec
Answer: B
Answer: B
Question: one gear of pulley rotates at a speed of 3 rev/sec another gear roates at 5 rev/sec. if both start together after how many seconds will they be together again
Options:
A)3 sec
B)5sec
C)15 sec
D)20 sec
E)25 sec
Rationale: 3 rotates 3,6,9,12,15
5 rotates 5,10,15
ans is 15
ANSWER:C
Answer: C
Question: A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 7 m, the volume of the box (in m3) is:
Options:
A)4830
B)5236
C)6420
D)8960
E)7960
Rationale: Clearly, l = (48 - 14)m = 34 m,
b = (36 -14)m = 22 m,
h = 8 m.
Volume of the box = (34 x 22 x 7) m3 = 5236 m3. Answer: Option B
Answer: B
Question: A king has 1000 bottles of wine,A queen wants to kill the king and sends a servant to poison the wine .Fortunately the king's guard's catch d servant after he has only poisoned one bottle and the guard don't know which bottle is poisoned .Furthermore it takes one month to have an effect,and there is an anniversary party coming up in 5 weeks time!the king decides he will get some of the prisoners in his vast dungeons to drink the wine.how many minimum prisoners does it required to sample the wine to find out the poisoned bottle so that the guests will still be able to drink the rest of the wine at his anniversary party in 5 weeks time?
Options:
A)1
B)499
C)500
D)999
E)10
Rationale: Since you need 10 digits to represent 1000 numbers in binary, you will need 10 prisoners.
Now the logic is this: Every bottle has a unique number from 1 to 1000 and a unique binary representation from 0000000001 to 1111101000.
Now you have 10 prisoners. Each bottle will be tasted by the prisoners depending on the binary representation of the bottle. Wherever there is 1, the bottle will be tasted by that prisoner (assuming units digit represents the 1st prisoner, tens digit the 2nd prisoner and so on...)
1st bottle is 0000000001 so it will be tasted by only the 1st prisoner.
2nd bottle is 0000000010 so it will be tasted by only the 2nd prisoner.
3rd bottle is 0000000011 so it will be tasted by the 1st and 2nd prisoners.
and so on...
1000th bottle is 1111101000 so it will be tasted by 4th, 6th, 7th, 8th, 9th and 10th prisoners.
At the end of a month, we see which prisoners die. Say, only the 3rd prisoner dies. This means the poisoned bottle number is 0000000100 = 3.
Say 1st, 7th and 9th prisoners die. This means the poisoned bottle number is 0101000001 = 321
ANS:E
Answer: E
Question: A train running at the speed of 90 km/hr crosses a pole in 6 seconds. What is the length of the train?
Options:
A)255
B)205
C)502
D)225
E)235
Rationale: Speed=(90 * 5/18) m/sec = (25) m/sec Length of the train = (Speed x Time) = (25 * 9) m
= 225 m.
Answer: D
Answer: D
Question: A train 180 m long is running with a speed of 55 km/hr. In what time will it pass a man who is running at 7km/hr in the direction opposite to that in which the train is going?
Options:
A)5.5
B)10.45
C)7
D)8
E)9.5
Rationale: Speed of train relative to man = 55+ 7 = 62 km/hr.
= 62 * 5/18 = 155/9 m/sec.
Time taken to pass the men = 180 *9/155 = 10.45 sec.
Answer: Option B
Answer: B
Question: The greatest number by which the product of three consecutive multiples of 2 is always
Options:
A)54
B)48
C)162
D)243
E)None of these
Rationale: Explanation:
2*4*6 = 48
Option B
Answer: B
Question: Danny and Steve are running towards each other, each one from his own house. Danny can reach Steve's house in 25 minutes of running, which is half the time it takes Steve to reach Danny's house. If the two started to run at the same time, how much time longer will it take Steve to reach the halfway point between their houses than Danny to reach the halfway point between their houses?
Options:
A)12.5 minutes.
B)25 minutes
C)35 minutes.
D)35 minutes
E)75 minutes
Rationale: If the distance between the two houses is D. Then
Speed of Danny = (D/25)
Speed of Steve = (D/50) [ Steve takes 50 minutes to reach Danny's house. double the time taken by Danny)
Obviously speed of Danny is Twice that of Steve.
Now in order to cover distance (D/2) [They meet in middle], Steve will take:
(D/2) / (D/50) = 25 minutes.
Distance is same and Danny's speed is twice of Steve. Thus he will take 12.5 minutes to cover this same distance.
Steve take 25-12.5 = 12.5 minutes longer.
A is the answer.
Answer: A
Question: 100 is increased by 50%. Find the final number.
Options:
A)100
B)110
C)150
D)155
E)160
Rationale: Final number = Initial number + 50%(original number) = 100 + 50%(100) = 100 + 50 = 150.
Answer C
Answer: C
Question: Of the four numbers, whose average is 50, the first is one-fourth of the sum of the last three. The first number is ?
Options:
A)28
B)29
C)11
D)48
E)40
Rationale: Explanation:
Let the first number be x,
Then, sum of the four numbers = x + 4x = 5x.
so, 5x/4 = 50 or x = (50 * 4) / 5 = 40
Answer: E
Answer: E
Question: While working alone at their constant rates, computer X can process 240 files in 12 hours, and computer Y can process 240 files in 6 hours. If all files processed by these computers are the same size, how many hours would it take the two computers, working at the same time at their respective constant rates, to process a total of 240 files?
Options:
A)3
B)3.5
C)4
D)4.5
E)5
Rationale: Both computers together process files at a rate of 240/12 + 240/6 = 20+40 = 60 files per hour.
The time required to process 240 files is 240/60 = 4 hours
The answer is C.
Answer: C
Question: What is the smallest integer that satisfies the inequality (x - 3)/ (x^2 - 8x - 20) > 0> 0?
Options:
A)-2
B)10
C)3
D)-1
E)0
Rationale: Explanatory Answer
Let us factorize the denominator and rewrite the expression as x−3 /(x−10)(x+2) > 0
Equate each of the terms of the expression to zero to identify the values of x that are relevant to test whether the inequality holds good.
The values that are relevant to us are x = 3, x = 10 and x = -2.
Let us arrange these values in ascending order: -2, 3 and 10.
The quickest way to solve inequalities questions after arriving at these values is verifying whether the inequality holds good at the following intervals.
Interval 1: x < -2.
Pick a value in that range and check whether the inequality holds good.
Let us take x = -10. When x = -10, x−3 /(x−10)(x+2) < 0; the inequality DOES NOT hold good in this interval.
Interval 2: -2 < x < 3.
Let us take x = 0. When x = 0, x−3/(x−10)(x+2) = 0−3 /(0−10)(0+2) > 0; the inequality holds good in this interval.
The least integer value that x can take if x > -2 is x = -1.
So, the correct answer is -1. Choice D.
Remember: We have to find out the least integer value. And we have arrived at -1.
Do, not waste time computing the entire range of values of x that satisfy the inequality.
Note: In any inequality question, when the question asks us to determine the intervals in which the inequality holds good, we have to eliminate values of x that will result in the denominator becoming zero.
Choice D
Answer: D
Question: If r = 199,999 and s = 991,999, which of the following is the units digit of r^4 + s^4?
Options:
A)0
B)1
C)2
D)8
E)9
Rationale: The exponents of 9 cycle between 9 (odd exponents) and 1 (even exponents).
Then the sum of r^4+s^4 will have the units digit of 1+1 = 2 as a units digit.
The answer is C.
Answer: C
Question: What is the area of a square with perimeter 4P ?
Options:
A) p^2
B) 4P
C) P^2/4
D) P/16
E) P^2/16
Rationale: Each side is p
A = (p)^2
Answer A
Answer: A