divelab/Sys2Bench huggingface dataset:
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
Options:
A)Rs. 1090
B)Rs. 1160
C)Rs. 1190
D)Rs. 1202
E)Rs. 1406
Rationale: S.P. = 85% of Rs. 1400 = Rs. (85/100)	x 1400 = Rs. 1190
Answer: Option C
Answer: C
Question: What is the units digit of (6!*4! + 6!*5!)/6?
Options:
A)1
B)0
C)2
D)3
E)4
Rationale: (6!*4! + 6!*5!)/6
=6!(4! + 5!)/6
=720 ( 24 + 120)/6
=(720 * 144)/6
= 720 * 24
Units digit of the above product will be equal to 0
Answer B
Answer: B
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5808, 6336
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Each one of remaining 5 is divisible by each one of 11, 3 and 4 and therefore, by 132.
ANSWER:B
Answer: B
Question: Little John had $8.50. He spent $1.25 on sweets and gave to his two friends $1.20 each. How much money was left?
Options:
A)$3.85
B)$4.85
C)$5.85
D)$2.85
E)$1.85
Rationale: John spent and gave to his two friends a total of
1.25 + 1.20 + 1.20 = $3.65
Money left
8.50 - 3.65 = $4.85
correct answer is B) $ 4.85
Answer: B
Question: On his deathbed, a father called upon his three sons and told them to distribute all his assets worth Rs. 52,500 in the ratio of 1/15 : 1/21 : 1/35 amongst themselves. Find the biggest share amongst the three portions.
Options:
A)Rs. 2,75,000
B)Rs. 2,45,000
C)Rs. 1,10,500
D)Rs. 1,13, 250
E)Rs. 1,15, 250
Rationale: The ratio of distribution should be:
21 x 35 : 15 x 35 : 15 x 21
= 147 : 105 : 63
= 7 : 5 : 3
The largest share will be worth:
7/15 x 525000 = Rs. 2,45,000
ANSWER:B
Answer: B
Question: In what proportion must rice at Rs 3.10 per kg be mixed with rice at Rs 3.75 per kg, so that the mixture be worth Rs 3.25 a kg?
Options:
A)7/3
B)5/3
C)10/3
D)3/7
E)11/5
Rationale: C.P of 1 kg of cheaper rice = Rs 3.10
C.P of 1 kg of expensive rice = Rs 3.75
the mixture be worth for 1 kg = Rs 3.25
By the alligation rule : Quantity of cheaper rice / Quantity of expensive rice
= (3.75 - 3.25)/(3.25 - 3.10)
= (0.50)/(0.15)
= 10/3
C
Answer: C
Question: If {x} is the product of all even integers from 1 to x inclusive, what is the greatest prime factor of {26} + {24}?
Options:
A)23
B)20
C)27
D)5
E)2
Rationale: Soln:
{26} + {24} = 26*{24} +{24} = 27*{24}
ANSWER:C
Answer: C
Question: Find the number that fits somewhere into the middle of the series. Some of the items involve both numbers and letters
Look at this series: J14, L16, __, P20, R22, ... What number should fill the blank?
Options:
A)S16
B)B29
C)N18
D)T34
E)M45
Rationale: C
N18
In this series, the letters progress by 2, and the numbers increase by 2.
Answer: C
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
Options:
A)986
B)1000
C)1200
D)1230
E)1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: E
Question: A man can row upstream at 45 kmph and downstream at 55 kmph, and then find the speed of the man in still water?
Options:
A)32 kmph
B)34 kmph
C)30 kmph
D)50 kmph
E)65 kmph
Rationale: US = 45
DS = 55
M = (45 + 55)/2 = 50
Answer:D
Answer: D
Question: If j and k are integers whose product is 400, which of the following statements must be true?
Options:
A)n + k > 0
B)n is not equal to k.
C)Either n or k is a multiple of 10.
D)If n is even, then k is odd.
E)If j is odd, then k is even.
Rationale: If j and k are integers whose product is 400, which of the following statements must be true?
A.n + k > 0n and k should have the same sign, but that means that they can also both be negative
B.n is not equal to k.20 x 20 = 400[i]
C.Either n or k is a multiple of 10. [i]25 x 16 = 400
D.If n is even, then k is odd.k can also be even since even x even will be even
E. If j is odd, then k is even.k must be even since odd x even = even
Answer: E
Question: A reduction of 40% in the price of bananas would enable a man to obtain 50 more for Rs.40, what is reduced price per dozen?
Options:
A)1.34
B)2.84
C)3.84
D)4.34
E)5
Rationale: 40*(40/100) = 16 --- 50
? --- 12 => Rs.3.84
Answer: C
Answer: C
Question: What least whole no. should be added to 532869 to make it divisible by 9?
Options:
A)5
B)6
C)9
D)10
E)11
Rationale: If a number is divisible by 9, the sum of its digits must be a multiple of 9.
Here, 5+3+2+8+6+9=33, the next multiple of 9 is 36.
3 must be added to 532869 to make it divisible by 9
C
Answer: C
Question: In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
Options:
A)63
B)12
C)45
D)72
E)36
Rationale: Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = = 63.
Ans: A
Answer: A
Question: Find the least number which when divided by 18,32,48,52 leaves remainder 14,28,44,48 respectively.
Options:
A)2845
B)3250
C)3740
D)4150
E)5140
Rationale: The difference of 18-14= 4 , 32-28 = 4 , 48-44= 4 , 52-48 = 4
LCM of 18,32,48,52 = 3744
Required number = 3744 - 4 = 3740
Answer is C
Answer: C
Question: If x is an even integer and y = 5x + 1, which of the following CANNOT be a divisor of y?
Options:
A)11
B)31
C)21
D)41
E)30
Rationale: x takes even values as 2,4,6,8.,
y=5x+1
x is an even term so 5x must be an even term when it adds with 1 so it must be a odd integer
30 didn't follows this condition ans is E
Answer: E
Question: Find the compound interest and the amount on Rs.8000 at 5% per annum for 4 years when C.I is reckoned yearly?
Options:
A)s.1261.05
B)s.1440.05
C)s.1185.05
D)s.1346.05
E)s.1724.05
Rationale: A = 8000(21/20)4
= 9724.05
= 8000
---------
1724.05
ANSWER:E
Answer: E
Question: M is a certain set of numbers with an average (arithmetic mean) of 10 and a standard deviation of 1.5. Q is a subset of M consisting of 5 terms. Exactly 80% of the numbers in Q are located within 2 standard deviations from the average of M. Which of the following could Q be?
Options:
A){3, 4, 5, 10, 14}
B){3, 7, 7, 10, 12}
C){3, 5, 5, 10, 16}
D){1, 5, 7, 10, 18}
E){5, 6, 7, 10, 12}
Rationale: Exactly 80% of the numbers in Q, so 4 out of 5 numbers are from 10 - 2*{SD} = 7 to 10 + 2*{SD} = 13.
A. {3, 4,5, 10, 14} --> only 3 numbers are in this range. Discard.
B. {3,7, 7, 10, 12} --> 4 numbers are in this range. OK.
C. {3,5, 5, 10, 16} --> only 1 number is in this range. Discard.
D. {1,5, 7, 10, 18} --> only 2 numbers are in this range. Discard.
E. {5, 6, 7, 10, 12} --> only 3 numbers are in this range. Discard.
Answer: B.
Answer: B
Question: How many numbers from 10 to 50 are exactly divisible by 9?
Options:
A)9
B)10
C)11
D)12
E)14
Rationale: 10/9 = 1 and 50/9 = 5 ==> 5 - 1 = 4. Therefore 4
Answer : E
Answer: E
Question: 3^11 + 3^11 + 3^11 =
Options:
A)3^12
B)3^13
C)3^30
D)9^10
E)9^30
Rationale: Since we have 3^11 added together 3 times, we can factor out a 3 and we get 3(3^11) which is equal to 3^12.
The answer is A.
Answer: A
Question: Find the area of a rhombus whose side is 25 cm and one of the diagonals is 30 cm?
Options:
A)600
B)881
C)767
D)261
E)121
Rationale: Consider the rhombus ABCD. Let the diagonals intersect at E. Since diagonals bisect at right angles in a rhombus.
BE2 + AE2 = AB2
252 = 152 + AE2 AE = √(625 - 225) = √400 = 20,
AC = 20 + 20 = 40 cm.
Area of a rhombus = 1/2 * d1d2
= 1/2 * 40 * 30 = 600 sq.cm.
Answer:A
Answer: A
Question: Two family reunions are happening at the Taj hotel, the Oates reunion and the Hall reunion. All 150 guests at the hotel attend at least one of the reunions. If 70 people attend the Oates reunion and 52 people attend the Hall reunion, how many people attend both reunions?
Options:
A) 2
B) 5
C) 10
D) 16
E) 28
Rationale: No of people in Oates reunion=70
No of people in Hall reunion=52
Attending both=x
All guests attend at least one.
Therefore, 150=70+52-(Both)
Both=28
Answer E
Answer: E
Question: A certain company has budgeted $1320 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $400, how much was the company under budget or over budget?
Options:
A)$70 under budget
B)$30 under budget
C)$30 over budget
D)$70 over budget
E)$180 over budget
Rationale: The budget for 3 months is (3/12)*$1320 = $330
The company is $70 over budget.
The answer is D.
Answer: D
Question: On his drive to work, Leo listens to one of three radio stations A, B or R. He first turns to A. If A is playing a song he likes, he listens to it; if not, he turns it to B. If B is playing a song he likes, he listens to it; if not, he turns it to R. If R is playing a song he likes, he listens to it; if not, he turns off the radio. For each station, the probability is 0.30 that at any given moment the station is playing a song Leo likes. On his drive to work, what is the probability that Leo will hear a song he likes?
Options:
A)0.027
B)0.09
C)0.417
D)0.657
E)0.9
Rationale: Probability he hears a song is like:
Tune to A and likes what he is hearing = 0.3
Tune to A, don't find he like what they are airing, then tune to B and likes what he finds there = 0.7 * 0.3 = 0.21
Tune to A, finds crap there, Tune to B, hears a similar crap, Tune to R and finally falls in love with the program = 0.7^2 * 0.3 = 0.147
Total = 0.657
Ans D
Answer: D
Question: For which of the following does n(a)−n(b)=n(a−b) for all values of a and b?
Options:
A)n(x)=x^2
B)n(x)=x/2
C)n(x)=x+5
D)n(x)=2x−1
E)n(x)=|x|
Rationale: To solve this easiest way is just put the value and see that if it equals or not.
with option 1. n(a) = a^2 and n(b) = b^2
so L.H.S = a^2 - b^2
and R.H.S = (a-b)^2 ==> a^2 + b^2 -2ab.
so L.H.S not equal to R.H.S
with option 2. n(a) = a/2 and n(b) = b/2
L.H.S = a/2 - b/2 ==> 1/2(a-b)
R.H.S = (a-b)/2
so L.H.S = R.H.S which is the correct answer.
answer:B
Answer: B
Question: How many factors greater than 50, which are multiples of 3, are possible in 8400?
Options:
A)41
B)31
C)21
D)11
E)01
Rationale: Prime factorisation of 8400- 2^4∗3∗5^2∗7
Number of factors of 8400 =
5*2*3*2=60
Number of factors of 8400 which are not multiple of 3
5*2*3=30
Number of factors of 8400 which are multiple of 3
60-30 = 30
Factors which are multiple of 3 but less than 50-
3,6,12,15,21,24,30,42,48
Total-9
Number of factors of 8400 which are multiple of 3 but more than 50 are
30-9 = 21
Answer:- C
Answer: C
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)23 sec
B)30 sec
C)27 sec
D)28 sec
E)29 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 500 * 3/50
= 30 sec.
Answer:B
Answer: B
Question: If X,Y is 20%,25% greater than Z then how much percentage is X smaller than Y?
Options:
A)3 1/13%
B)3%
C)3 11/13%
D)4%
E)None of these
Rationale: Explanation:
X = 125%
Y = 130%
Z = 100%
X-Y/Y * 100 = 5/130 * 100
= 500/130 %
= 3 11/13% smaller than Y
Answer: Option C
Answer: C
Question: Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?
Options:
A)2 <= 3x+4 <= 6
B)24 <= 34x+4 <= 6
C)2 <= 356x+4 <= 6
D)2 <= 378x+4 <= 6
E)2 <= 357x+4 <= 6
Rationale: The key words in the stem are:a singleline segment offinite length
Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.
Answer: A.
Answer: A
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 500 resolutions.
Options:
A)287 m
B)704 m
C)168 m
D)278 m
E)107 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 500 resolutions.
= 500 * 2 * 22/7 * 22.4
= 70400 cm
= 704 m
Answer: B
Answer: B
Question: The speed of a car is 70 km in the first hour and 90 km in the second hour. What is the average speed of the car?
Options:
A)79 kmph
B)80 kmph
C)34 kmph
D)23 kmph
E)14 kmph
Rationale: S = (70 + 90)/2
= 80 kmph
Answer:B
Answer: B
Question: A loan has a variable interest rate that fluctuates between 7% and 10% of the base payment per month. If base payments remain at $300 each month and an additional monthly surcharge of 1% is added to the combined (base + interest), what would be the greatest possible payment due in any given month?
Options:
A)$330.00
B)$331.00
C)$332.30
D)$333.30
E)$334.60
Rationale: The maximum interest in one month is 10%*$300=$30.
The combined payment (base plus interest) is $300 + $30 = $330.
The greatest possible payment is: 1.01*$330=$333.30.
The answer is D.
Answer: D
Question: 4 bells first begin to toll together with an intervals of 5, 10, 15 & 20 sec. How many times does they toll together in an hr?
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: 5|5, 10, 15, 20
2|1, 2, 3, 4
|1, 1, 3, 2
L.C.M of 5, 10, 15, 20 is 60
60 times
B
Answer: B
Question: Find 30 % of 240
Options:
A)72
B)94
C)86
D)74
E)110
Rationale: We know that R % of m is equal to R/100 × m.
So, we have 30 % of 240
30/100 × 240
= 72
Answer:A
Answer: A
Question: If X is to be chosen at random from the set {5,7,4,3,8} and Y is to be chosen at random from the set {6,3,4,2}, what is the probability that XY will be odd?
Options:
A)12
B)8
C)11
D)6
E)1
Rationale: Method-1
xy will be odd when
1) x is odd and y is even, Probability of x odd is (3/5) and Probability of y even is (3/4), so Probability of Case(1) = (3/5)*(3/4) = (15/20)=(3/4)
2) x is even and y is odd, Probability of x even is (2/5) and Probability of y odd is (1/4), so Probability of Case(2) = (2/5)*(1/4) = (2/20)
3) x is odd and y is odd, Probability of x odd is (3/5) and Probability of y odd is (1/4), so Probability of Case(1) = (3/5)*(1/4) = (3/20)
Total Favorable Probability = (15/20)+(2/20)+(3/20) = (20/20) = 1
Answer: option E
Answer: E
Question: In an entrance exam, 3 marks is awarded for every correct answer and (-1) for every wrong answer. If a student gets 38 marks after attempting all questions, find the number of questions answered correctly if the total questions were 70.
Options:
A)38
B)40
C)27
D)43
E)56
Rationale: Explanation:
Let x be the number of questions answered correctly. Hence, number of questions whose answer were wrong = (70 – x)
3*x + (70 – x)*(-1) = 38
4x = 38 + 70 = 108
x = 27
ANSWER C
Answer: C
Question: On 8th Feb, 2005 it was Tuesday. What was the day of the week on 8th Feb, 2004?
Options:
A)Sunday
B)Friday
C)Saturday
D)Monday
E)Tuesday
Rationale: Given that 8th Feb, 2005 was Tuesday
Number of days from 8th Feb, 2004 to 7th Feb, 2005 = 366 (Since Feb 2004 has 29 days as it is a leap year)
366 days = 2 odd days
Hence 8th Feb, 2004 = (Tuesday - 2 odd days) = Sunday
Answer:A
Answer: A
Question: A box contains 6 black, 8 red and 4 green marbles. 2 marbles are drawn from the box at random. What is the probability that both the marbles are of the same color?
Options:
A)49/153
B)18/153
C)49/153
D)40/153
E)24/72
Rationale: Explanation:
Total marbles in a box = 6 black + 8 red +4 green marbles = 18 marbles
2 marbles are drawn from 18 marbles at random. Therefore,
n(S) = 18C2 = 153 ways
Let A be the event that 2 marbles drawn at random are of the same color. Number of cases favorable to the event A is
n(A) = 6C2 + 8C2 + 4C2 = 15+28+6= 49
Therefore, by definition of probability of event A,
P(A) = n(A)/n(S) = 49/153
ANSWER:A
Answer: A
Question: The population of a town is 10000. It increases annually at the rate of 20% p.a. What will be its population after 3 years?
Options:
A)14300
B)17280
C)14500
D)14600
E)15400
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 × 120/100^3 = 17280
B)
Answer: B
Question: There was a match to be held.And 100 nations were to participate in that match.It was totally an elimination match,that is if a team loses a match it must be eliminated.Find out the total number of matches played to find out the grand winner?
Options:
A)96
B)97
C)98
D)99
E)92
Rationale: 100-1=99 as every match will eliminate one team.
ANSWER:D
Answer: D
Question: Find the missing figures :
?% of 60 = 2.125
Options:
A)8.54
B)6.54
C)8.7
D)3.54
E)4.54
Rationale: (i)	Let x% of 60 = 2.125. Then , (x/100)*60 = 2.125
X = (2.125 * 100/60) = 3.54
Answer is E.
Answer: E
Question: Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word SUCCESS could be arranged to create a seven-letter code?
Options:
A)6!
B)6! − (3! + 2!)
C)7!/(3! × 2!)
D)7!/(3! + 2!)
E)8!/(2! x 2!)
Rationale: Number of letters in word 'SUCCESS' = 7.
The letters 'S' and 'C' appear 3 times and 2 times respectively in the word 'SUCCESS'.
Therefore the mathematical solution for number of ways that the letters of the word SUCCESS can be arranged to create seven-letter code
= 7!/(3!*2!)
Answer:C
Answer: C
Question: The average of first 32 natural numbers is?
Options:
A)16.5
B)17.5
C)18.4
D)15.4
E)15.1
Rationale: Sum of 32 natural no. = 1056/2 = 55
Average = 528/32 = 16.5
Answer:A
Answer: A
Question: A boat ma goes 2km against the current of the stream in 1 hr and goes 1 km along the current in 10 min. how long will it take to go 8 km in stationary water
Options:
A)40 min
B)1hr
C)1hr 15 min
D)1hr 30 min
E)2 hr
Rationale: rate down stream=(1/10*60)km/hr=6km/hr
rate up stream=2km/hr
speed still water =1/2(6+2)=4km/hr
required time =(8/4)=3 hr
Answer(E)
Answer: E
Question: A rectangular lawn of length 50 m and breadth 35 m is to be surrounded externally by a path which is 2 m wide. Find the cost of turfing the path at the rate of $3 per m².
Options:
A)$1008
B)$1031
C)$1028
D)$1068
E)$1088
Rationale: Length of the lawn = 50 m
Breadth of the lawn = 35 m
Area of the lawn = (50 × 35) m²
= 1750 m²
Length of lawn including the path = [50 + (2 + 2)] m = 54 cm
Breadth of the lawn including the path = [35 + (2 + 2)] m = 39 m
Area of the lawn including the path = 54 × 39 m² = 2106 m²
Therefore, area of the path = (2106 - 1750) m² = 356 m²
For 1 m², the cost of turfing the path = $ 3
For 356 m², the cost of turfing the path = $3 × 356 = $1068
ANSWER : D
Answer: D
Question: A boy can reach a certain place in 45 hours. If he reduces his speed by 1/30th, he goes 3 km less in that time. Find his speed.
Options:
A)2 km/hr.
B)6 km/hr
C)8 km/hr
D)14 km/hr
E)None of these
Rationale: Explanation :
Solution: Let the speed be x km/hr. then,
45x - (45 * 29x/30) = 3
=> 3/2X =3
X=2
A
Answer: A
Question: One-fourth of the light switches produced by a certain factory are defective. Four-fifths of the defective switches are rejected and 1/20 of the non defective switches are rejected by mistake. If all the switches not rejected are sold, what percent of the switches sold by the factory are defective?
Options:
A)4.4%
B)5.5%
C)6.6%
D)11.3%
E)16.2%
Rationale: 1/4 of the switches are defective.
The defective switches that are not rejected are 1/5*1/4 = 1/20 = 4/80 of all switches.
The non defective switches that are sold are 3/4*19/20 = 57/80 of all switches.
The percent of switches sold that are defective is 4/61 = 6.6%
The answer is C.
Answer: C
Question: If P(A) = 2/15, P(B) = 4/15, and P(A âˆª B) = 6/15 Find P(B|A)
Options:
A)1/2
B)2/3
C)3
D)4/5
E)4/7
Rationale: P(B|A) = P(A âˆª B)/P(A)
P(B|A) = (6/15)/(2/15) = 3.
C
Answer: C
Question: A train running at the speed of 60 km/hr crosses a pole in 12 seconds. Find the length of the train.
Options:
A)150
B)278
C)179
D)200
E)191
Rationale: :
Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 12 = 200 meter
Answer:D
Answer: D
Question: The average number of visitors of a library in the first 4 days of a week was 58. The average for the 2nd, 3rd, 4th and 5th days was 60.If the number of visitors on the 1st and 5th days were in the ratio 7:8 then what is the number of visitors on the 5th day of the library?
Options:
A)17
B)17
C)64
D)19
E)01
Rationale: If number of visitors on 1st, 2nd, 3rd, 4th & 5th day are a, b, c, d & e respectively, then
a + b + c + d = 58 × 4 = 232 ----(i) &
b + c + d + e = 60 × 4 = 240 ----(ii)
Subtracting (i) from (ii), e – a = 8 ---(iii)
Given
a/e=7/8 ---(iv)
So from (iii) & (iv) a=56, e=64
Answer:C
Answer: C
Question: A computer manufacturer produces a certain electronic component at a cost of $70 per component. Shipping costs for delivering the components are $4 per unit. Further, the manufacturer has costs of $14,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 250 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
Options:
A)132
B)138
C)144
D)128
E)116
Rationale: $14500 is a fixed cost
Each component is $74 ($70 to produce, $4 to ship)
Manufacturer will be producing and selling 250 components
so therefore the equation to find price would be
250*p = 14500+(250*70)+(250*4)
p = (14500+17500+1000)/250
p = 132
Answer:A
Answer: A
Question: The sum of three consecutive even numbers is 30. Find the middle number of the three?
Options:
A)14
B)16
C)18
D)25
E)34
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 30
6P = 30 => P = 5.
The middle number is: 5P = 25.
ANSWER:D
Answer: D
Question: If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is L:
Options:
A)L=1
B)L=2
C)L=3
D)L=4
E)5
Rationale: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.
Hence p/48 should resolve to a integer.
48 -- > 2^4 * 3.
Hence p should have atleast 2^4*3 for p/48 to resolve to a int.
The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).
Answer: B
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 15 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
Options:
A)$207
B)$210
C)$230
D)$213
E)$215
Rationale: Final price = (1+15/100) * Original Price
= 1.15 * Original Price
From options given only 230 is divisible by 1.10 as it is stated OP is whole dollar amount.
Hence C
Answer: C
Question: How many positive three-digit integers are divisible by both 3 and 7?
Options:
A)43
B)45
C)47
D)50
E)52
Rationale: A number to be divisible by both 3 and 7 should be divisible by the least common multiple of 3 and 7 so by 21.
Multiples of 21 between 100 and 999, inclusive is
(last-first)/multiple+1=(987-105)/21+1=42+1=43
Answer: A.
Answer: A
Question: Three partners A,B,C start a business.A invested 3000 for 8 month,B invested
4000 for 9 month.and C invested 5000 for 1 years.at the end of year there is total profit of 15000 rs.what is profit share of B?
Options:
A)3000
B)4500
C)4000
D)4200
E)3500
Rationale: ratio of A,B,C investment=(3000*8):(4000*9):(5000*12)
=24000:36000:60000=2:3:5.
Total annual profit=15000 rs.
profit share of B=15000*3/10=4500rs.
answer B
Answer: B
Question: If p/q = 5/4 , then 2p+q= ?
Options:
A)12
B)14
C)13
D)15
E)16
Rationale: let p=5, q=4 then 2*5+4=14
so 2p+q=14.
ANSWER:B
Answer: B
Question: A sum of money at simple interest amounts to $ 815 in 3 years and to $854 in 4 years. The sum is:
Options:
A)$153
B)$698
C)$398
D)$549
E)$675
Rationale: B
$698
S.I. for 1 year = $(854 - 815) = $39.
S.I. for 3 years = $(39 x 3) = $117.
Principal = $(815 - 117) = $698.
Answer: B
Question: When n is divided by 19, the remainder is 7. Find thee difference between previous remainder and the remainder when 18n is divided by 9 ?
Options:
A)7
B)5
C)0
D)3
E)9
Rationale: Let n=7 (leaves a remainder of 7 when divided by 19)
18n = 18(7) =126, which leaves a remainder of 0 when divided by 9.
difference = 7 - 0 = 7.
Answer A
Answer: A