divelab/Sys2Bench huggingface dataset:
Question: If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?
Options:
A)1/4
B)3/8
C)1/2
D)5/8
E)3/4
Rationale: total nos of ways in which we can choose n = 96
n(n + 1)(n + 2) will be divisible by 8?
case 1: n = odd then n+2 =odd & n+1 will be even i.e this needs get divided by 8, hence is a multiple of 8 so we have 8..96 = 12 multiples to fill the n+1 pos hence 12 ways
case 2: n is even then n+2 will be even & the product will be divisible by 24 & thus 8
so nos of values that can be used for n= 2....96 (all even nos) i.e 48 nos
total = 48+12 =60 ways
so reqd P =60/96 =5/8;
ANSWER:D
Answer: D
Question: There is 50% increase in an amount in 6 years at S.I. What will be the C.I. of Rs. 12,000 after 3 years at the same rate?
Options:
A)2160
B)3120
C)17988
D)6240
E)5240
Rationale: Let P = Rs. 100. Then, S.I. Rs. 50 and T = 6 years.
R = (100 * 50)/(100 * 6) = 10% p.a.
Now, P = Rs. 12000, T = 3 years and R = 8.33% p.a.
C.I. = [12000 * {(1 + 8.33/100)3 - 1}]
= Rs. 17988
ANSWER:C
Answer: C
Question: The average marks obtained by 50 candidates in a certain examination is 40.Find the total marks.
Options:
A)1800
B)2000
C)1640
D)2200
E)2400
Rationale: Following the above formula, we have the total marks =50*40=2000
Answer is B
Answer: B
Question: If 20% of (x-y) = 15% of (x+y), then what percent of x is y?
Options:
A)50.5%
B)44.4%
C)22.2%
D)14.3%
E)25%
Rationale: 20% of (x-y) = 15% of (x+y)
20/100 (x-y) = 15/100 (x+y)
5x = 35y
Required percentage = y/x *100 = 5y/35y * 100 = 14.28%
Answer is D
Answer: D
Question: 4,6,12,24,36,48....
Options:
A)58
B)60
C)61
D)62
E)63
Rationale: 2*2=4
3*2=6
6*2=12
12*2=24
18*2=36
24*2=48
30*2=60
ANSWER:B
Answer: B
Question: 30 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.
Options:
A)190
B)200
C)210
D)220
E)435
Rationale: or, if there are n persons then no. of shakehands = nC2 = 30C2 = 435
ANSWER:E
Answer: E
Question: If a - b = 3 and a2 + b2 = 29, find the value of ab.
Options:
A)10
B)12
C)13
D)15
E)18
Rationale: 2ab = (a2 + b2) - (a - b)2
= 29 - 9 = 20
ab = 10.
answer :A
Answer: A
Question: A Prototype fuel-efficient car (P-Car) is estimated to get 80% more miles per gallon of gasoline
than does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type
of gasoline that costs 20% less per gallon than does the gasoline used by a T-Car. If the two
cars are driven the same distance, what percent less than the money spent on gasoline for the
T-Car is the money spent on gasoline for the P-Car?
Options:
A)16 2/3%
B)33 1/3 %
C)50%
D)55.56%
E)66 2/3 %
Rationale: Assumption
Miles/Gallon
T = 100
P = 180 ( 80% more)
$/gallon
T = 100
P = 80 (20% less)
Miles
100 for both
Cost = (Miles X $/ Gallon)/ M/gallon
T = 100
P = 44.44
Hence 100 - 44.44 =55.56%
Ans D
Answer: D
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
Options:
A)14
B)17
C)19
D)22
E)24
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer : A
Answer: A
Question: he total marks obtained by a student in Physics, Chemistry and Mathematics is 110 more than the marks obtained by him in Physics. What is the average mark obtained by him in Chemistry and Mathematics?
Options:
A)55
B)65
C)75
D)85
E)95
Rationale: Let the marks obtained by the student in Physics, Chemistry and Mathematics be P, C and M respectively.
P + C + M = 110 + P
C + M = 110
Average mark obtained by the student in Chemistry and Mathematics = (C + M)/2 = 110/2 = 55.
ANSWER:A
Answer: A
Question: The investment of A, B, and C in a business are in the ratio 3:1:4. The total investment is Rs. 60,000. Find the investment made by each.
Options:
A)22500, 7500, 30000
B)22000, 8000, 30000
C)23500, 7500, 29000
D)23000, 8500, 28500
E)23000, 8000, 29000
Rationale: ratio of the investment is 3:1:4
Total investment =60000
so, 8x = 60000 ie)x =7500
so the investment of A, B,C are : A's investment 3x = 22500 B's investment x = 7500 C's investment 4x =30000
ANSWER:A
Answer: A
Question: On dividing 13698 by a certain number, we get 89 as quotient and 14 as remainder. What is the divisor?
Options:
A)743
B)154
C)852
D)741
E)785
Rationale: Divisor *quotient+remainder=dividend
divisor=(dividend)-(remainder)/quotient
(13698-14)/89=154
Answer(B)
Answer: B
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
Options:
A)218
B)150
C)167
D)166
E)112
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: B
Answer: B
Question: In a company with 48 employees, some part-time and some full-time, exactly (1/3) of the part-time employees and (1/4) of the full-time employees take the subway to work. What is the greatest possible number Q of employees who take the subway to work?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: P/3 + F/4 = P/3 + (48-P)/4 = 12 + P/2
P/3 + F/3 = (P+F)/3 = 48/3 = 16
P/4 + F/4 = 12
P/3 + F/3 > P/3 + F/4 > P/4 + F/4
--> 16> 12 + P/12 > 12
GREATEST Possible Q: 12 + p/12 = 15 --> p = 36 ( integer --> good)
15 or D is the answer
Answer: D
Question: In the junior basketball league there are 15 teams, 1/3 of them are bad and ½ are rich. What can't be the number of teams that are rich and bad?
Options:
A)4.
B)6.
C)7.
D)8.
E)9.
Rationale: total teams =15
bad teams=(1/3)*15=5
rich teams=8
so maximum value that the both rich and bad can take will be 8. so E= 9 can not be that value.
ans E.
Answer: E
Question: A man is 26 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
Options:
A)16
B)19
C)15
D)24
E)10
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 26) years.
(x + 26) + 2 = 2(x + 2)
x + 28 = 2x + 4
=> x =24 .
Answer: D
Answer: D
Question: Two numbers are in the ratio of 5:7. If 25 be subtracted from each, they are in the ratio of 35:59. Find the numbers?
Options:
A)60,89
B)60,88
C)60,86
D)60,84
E)60,81
Rationale: (5x-25):(7x-25) = 35:59
x = 12 => 60,84
Answer: D
Answer: D
Question: If u r genius solve it:-
40 * 14 = 11
30 * 13 = 12
20 * 12 = 6
10 * 11 = 2
9 * 10 = ?
Options:
A)2
B)4
C)6
D)9
E)10
Rationale: Logic :
40*14=560=5+6+0=11
30*13=390=3+9+0=12
20*12=240=2+4+0=6
10*11=110=1+1+0=2
So 9*10=90=9+0=9
Answer : D
Answer: D
Question: The simple interest accrued on an amount of Rs.49500 at he end of three is Rs.17820. What would be the compound interest accured on the same amount at teh same rate in the same period? (Round off your answer to two decimal places)
Options:
A)20043.94
B)38933.3
C)93832.39
D)29334.93
E)20483.33
Rationale: Let the rate of interest be R% p.a.
(49500)(3)(R)/100 = 17820
495R = 5940
R = 12
CI on Rs.49500 at 12% p.a. for three years
= 49500{[1 + 12/100]3 - 1} = 69543.936 - 49500 = Rs.20043.94
when rounded off to two decimal places.
Answer: A
Answer: A
Question: Bucket P has thrice the capacity as bucket Q. It takes 80 turns for bucket P to fill the empty drum. How many turns it will take for both the buckets P and Q, having each turn together to fill the empty drum?
Options:
A)30
B)45
C)60
D)80
E)100
Rationale: Explanation:
Let capacity of Q =1 litre.
Then, capacity of P =3 litre.
Given that it takes 80 turns for bucket P to fill the empty drum.
=> capacity of the drum =80×3=240 litre.
Number of turns required if both P and Q are used having each turn together
240/3+1 =60 litre.
Answer: Option C
Answer: C
Question: 5 men are equal to as many women as are equal to 8 boys. All of them earn Rs.90 only. Men’s wages are?
Options:
A)6Rs
B)8Rs
C)9Rs
D)1Rs
E)2Rs
Rationale: 5M = xW = 8B
5M + xW + 8B ----- 90 Rs.
5M + 5M + 5M ----- 90 Rs.
15M ------ 90 Rs. => 1M =6Rs.
Answer:A
Answer: A
Question: What is the sum of the different positive prime factors of 350?
Options:
A)10
B)11
C)14
D)16
E)18
Rationale: 350
35*10 --> 5*7*2*5 --> 5+7+2=14. Remember its asking for the DIFFERENT positive prime factors of 350.
C
Answer: C
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)328
B)279
C)245
D)288
E)211
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.Answer: C
Answer: C
Question: The manufacturing cost of a shoe is Rs.190 and the transportation lost is Rs.500 for 100 shoes. What will be the selling price if it is sold at 20% gains
Options:
A)s 234
B)s 216
C)s 220
D)s 210
E)s 217
Rationale: Explanation :
Total cost of a watch = 190 + (500/100) = 195.
Gain = 20% => SP = 1.2CP = 1.2 X 195 = 234
Answer : A
Answer: A
Question: One night 19 percent of the female officers on a police force were on duty. If 152 police officers were on duty that night and half of these were female officers, how many female officers were on the police force?
Options:
A)300
B)350
C)400
D)450
E)500
Rationale: Let x be the number of female police officers on the police force.
The number of female police officers on duty was 76.
0.19x = 76
x = 400
The answer is C.
Answer: C
Question: If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 14 is subtracted and divided by 10?
Options:
A)4
B)7
C)8
D)5
E)3
Rationale: Explanation:
Let the number be x. Then,
(x - 5)/7 = 7 => x - 5 = 49
x = 54
.: (x - 14)/10 = (54 - 14)/10 = 4
Answer: Option A
Answer: A
Question: 200 is what percent of 50?
Options:
A)0.2%
B)2%
C)5%
D)20%
E)400%
Rationale: 200= x*50/100
x = 400%
Ans; E
Answer: E
Question: 3-5*6+2=
Options:
A)A)2
B)B)-13
C)C)-18
D)D)-17
E)E) -25
Rationale: 3-5*6+2 = 5-30 = -25...
so the answer is -25... E
Answer: E
Question: What is the remainder of W=3^19 when divided by 10?
Options:
A)0
B)1
C)5
D)7
E)9
Rationale: I looked for patterns:
^2 - units digit 9
^3 - units digit 7
^4 - units digit 1
^5 - units digit 3
hence, we can see that when raised to a power which is multiple of 4, the units digit is 1, and when to an even power not multiple of 4, the units digit is 9
and we can then see:
^16 - units digit 1, or
^18 - units digit 9
and ^19 - units digit 7
therefore, W=when divided by 10, the remainder must be 7.D
Answer: D
Question: A, B and C enter into a partnership. A invests 3 times as much as B invests and 2/3 of what C invests. At the end of the year, the profit earned is Rs. 11000. What is the share of C?
Options:
A)Rs. 2250
B)Rs. 3000
C)Rs. 6750
D)Rs. 5625
E)None of these
Rationale: Explanation:
Let the investment of C be Rs. x.
The inverstment of B = Rs.(2x/3)
The inverstment of A = Rs. (3 × (2/3)x) = Rs. (2x)
Ratio of capitals of A, B and C = 2x : 2x/3 : x = 6 : 2 : 3
C's share = Rs. [(3/11) × 11000] = Rs. 3000
Answer: Option B
Answer: B
Question: If a car had traveled 40 kmh faster than it actually did, the trip would have lasted 30 minutes less. If the car went exactly 120 km, at what speed did it travel?
Options:
A)50 kmh
B)60 kmh
C)70 kmh
D)80 kmh
E)90 kmh
Rationale: Time = Distance/Speed
Difference in time = 1/2 hrs
120/x - 120/(x + 40) = 1/2
Substitute the value of x from the options. --> x = 80 --> 120/80 - 120/120 = 3/2 - 1 = 1/2
Answer: D
Answer: D
Question: There are 8 men and 4 chairs. In how many ways men can occupy the chairs?
Options:
A)1760
B)8400
C)1680
D)1740
E)1800
Rationale: total men = 8
total chairs = 4
1st chair can be occupy in 8ways
2nd chair can be occupy in 7ways
3rd chair can be occupy in 6ways
4th chair can be occupy in 5ways
total number of ways = 8*7*6*5 = 1680 ways
correct option is C
Answer: C
Question: A new beverage, which is a mixture of grape juice and apple juice, is being tested. The test container of 800 milliliters is 15% grape juice. If the response to the beverage causes the maker to increase the percentage of grape juice in the container to 20%, how much grape juice will be added?
Options:
A)30
B)40
C)50
D)120
E)160
Rationale: So, (120+k)/(800+k)=20/100
Or, (120+k)/(800+k)=15
Or, 600+5k=800+k
Or, 4k=200
Or, k=50
Or, k=50k=50
So, 50 ml of Grape juice , must be added , answer must be (C)
Answer: C
Question: Of the 400 members at a health club, 260 use the weight room and 310 use the pool. If at least 60 of the members do not use either, then the number of members using both the weight room and the pool must be between:
Options:
A)40 to 100
B)240 to 280
C)230 to 260
D)220 to 300
E)200 to 260
Rationale: W=260
P=310
ALL=400
N(NEITHER)=AT LEAST 60
BOTH=?
W+P-BOTH+N=ALL
260+310-BOTH+60=400
BOTH=230
now pay attention to the fact, that both at most can be 260, since W=260
C
Answer: C
Question: If each digit in the set A = {1, 2, 3, 4, 5} is used exactly once, in how many ways can the 5 digits be arranged?
Options:
A)6
B)24
C)72
D)96
E)120
Rationale: Use the slot method for all the possible arrangements:
we have 5 options for the 1st slot, 4 for the 2nd, 3 for 3rd , 2 for 4th and 1 for the 5th, giving the total number of
arrangements = 5*4*3*2*1 = 120,
E is the correct answer.
Answer: E
Question: A sum was put at simple interest at certain rate for 3 years. Had it been put at 1% higher rate it would have fetched Rs. 72 more. The sum is: A. Rs. 2,400 B. Rs. 2,100 C. Rs. 2,200 D.Rs. 2,480
Options:
A)2000
B)2100
C)2200
D)2300
E)2400
Rationale: 1 percent for 3 years= 72
1 percent for 1 year = 24
=> 100 percent = 2400
ANSWER:E
Answer: E
Question: The average age of 4 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
Options:
A)22
B)30
C)99
D)26
E)27
Rationale: total age increased = (8 * 2) years = 8 years.
Sum of ages of two new men = (21 + 23 + 8) years = 52 years
Average age of two new men = (52/2) years = 26 years.
Answer: D
Answer: D
Question: A particular store purchased a stock of turtleneck sweaters and marked up its cost by 20%. During the New Year season, it further marked up its prices by 25% of the original retail price. In February, the store then offered a discount of 12%. What was its profit on the items sold in February?
Options:
A)27.5%
B)32%
C)35%
D)37.5%
E)40%
Rationale: Assume the total price = 100x
Price after 20% markup = 120x
Price after 25%further markup = 1.25*120x = 150x
Price after the discount = 0.88*150x = 132x
Hence total profit = 32%
Option B
Answer: B
Question: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
Options:
A)15y/18
B)6y/5
C)18y/5
D)60y
E)3600000y
Rationale: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
We need to find an equation with y in the answer...
convert all measurements so they are alike (i.e. convert km to m, seconds to hours, etc)
Speed = y/t
y meters/second
(3600) x meters/hour
Speed = x/t
x KM/hour
Speed = x(1000m)/hour
x(1000meters)/hour = (3600) x meters/hour
x(1000)/1hour = y(3600) / 1 hour
x(1000) = y(3600)
x = 3.6y
Answer: C. 18y/5
Answer: C
Question: On average, the bottle-nosed dolphin comes up for air once every three minutes; the beluga whale, a close relative, comes up for air on average once every nine minutes. The number of times a bottle-nosed dolphin would come up for air in a 24 hour period is approximately what percent greater than the number of times a beluga whale would come up for air in that same period?
Options:
A)150%
B)200%
C)250%
D)300%
E)350%
Rationale: Dolphin once in 3 min;
Beluga once in 9 min;
So, dolphin comes up 3 times frequently than beluga, which is 300% (9-3)/2*100.
Answer: D.
Answer: D
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Options:
A)16 kmph
B)19 kmph
C)14 kmph
D)11 kmph
E)13 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream
= (2+1)/(2-1) = 3/1
= 3:1
Speed of the stream
= 42/3 = 14 kmph.
Answer: C
Answer: C
Question: Tough and Tricky questions: Exponents.
If a and b are positive integers and x = 5^a and y = 4^b, which of the following is a possible units digit of xy?
Options:
A)1
B)4
C)5
D)7
E)0
Rationale: Only Units digit of X and Y contribute to the Units digit of XY.
Finding all values ofXfor positive values ofa
When,
a=1; X=5
a=2; X=25
a=3; X=125........ Units digit repeat in a cycle of 5......
Similarly, Finding all values ofYfor positive values ofb
When,
b=1; Y=4
b=2; Y= 16
b=3; Y= 64....... Units digit repeat in cycle of 4,6,4....
So, possible value of Units digit of XY can be found by considering all possibilities of Units digit of X and Y
When X=5 and Y=4: Units digit of XY = 20
When X=5 and Y=6: Units digit of XY = 30
Only one possibility for Units digit of XY i.e. 0.
therefore answer is E
Answer: E
Question: Two dice are rolled. What is the probability the sum will be greater than 11?
Options:
A)1/9.
B)1/12.
C)1/36.
D)1/6.
E)1/5.
Rationale: Combinations possible: (6,6) = 1
Total combinations possible: 6*6=36
Answer = 1/36 Option C.
Answer: C
Question: A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs.3500, A will get:
Options:
A)Rs.1200
B)Rs.1500
C)Rs. 2100
D)Rs.2000
E)None of these
Rationale: Explanation:
Ratio of working days of A : B = 10 : 15
Therefore, their wages ratio = reverse ratio = 15 : 10
Therefore, A will get 15 units of ratio
Total ratio = 25
1 unit of ratio =3500/25 = 140
So, A’s amount = 120 × 15 = Rs.2100.
Answer: Option C
Answer: C
Question: A train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the train is going?
Options:
A)7 sec
B)8 sec
C)10 sec
D)12 sec
E)14 sec
Rationale: Speed of the train relative to man = (59 + 7) kmph
= 66 *5/18 m/sec = 55/3 m/sec.
Time taken by the train to cross the man = Time taken by it to cover 220 m at (55/3) m / sec
= (220 *3/55) sec = 12 sec
Answer : D.
Answer: D
Question: An investment of $5000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $5000 increased to $20000 by earning interest. In how many years after the initial investment was made the $5000 have increased to $40000 by earning interest at that rate?
Options:
A)16
B)12
C)20
D)24
E)18
Rationale: In 12 years the investment quadrupled (from $5,000 to $40,000).
Thus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $20,000 to $40,000).
Therefore, 12+6=18 years are needed $5,000 to increase to $40,000.
Answer: E.
Answer: E
Question: All factors of a positive integer B are multiplied and the product obtained is B^3. If B is greater than 1, how many factors does B have?
Options:
A)2
B)3
C)6
D)7
E)8
Rationale: The question can be done in seconds if you understand the properties of factors of a number. Note that every distinct factor of a number which is not a perfect square has a complementary factor.
For example,
Factors of 6: 1, 2, 3, 6
1 has a complementary factor 6 such that 1*6 = 6 (the original number)
2 has a complementary factor 3 such that 2*3 = 6 (the original number)
So if you have a number, n, which is not a perfect square, and start multiplying its factors, you will get n to a certain power. the power will half of the number of factors. For example, 6 has 4 factors and when you multiply all 4 factors, you get 6^2 (2 is half of 4).
So if you know that the product of all factors is B^3, it means there must have been twice the number of factors i.e. 3*2 = 6 factors.
C)
Answer: C
Question: he average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 24 years. Find the average age of the women?
Options:
A)37
B)74
C)30
D)34
E)35
Rationale: 20 + 24 + 8 * 2
= 60/2
= 30
Answer:C
Answer: C
Question: How many positive integers less than 30 are either a multiple of 2, an odd prime number, of the sum of a positive multiple of 2 and an odd prime?
Options:
A)29
B)28
C)27
D)25
E)23
Rationale: Any odd number can be expressed as 2k+1 or 2k+(3-2) or 2(K-1)+3.
Thus, with the prime number 3,
we can express all the odd numbers.
Since, 1 i is the only number that cannot be expressed,
answer is numbers <30 =29-1.
ANSWER:B
Answer: B
Question: How many six-digit numbers that do not contain the digits 5 or 8 are there?
Options:
A)483224
B)156444
C)229376
D)816416
E)316544
Rationale: We can have 7 digits ( 1,2,3,4,6,7,9) for the first place ( hundred thousand's place).
and similarly 8 digits for ten thousands, thousands, hundred's, tenth's and unit digit. ( 0,1,2,3,4,6,7,9)
So in total 7*8*8*8*8*8= 229376
Hence C
Answer: C
Question: A train covers a distance of 12 km in 10 min. If it takes 10 sec to pass a telegraph post, then the length of the train is?
Options:
A)200
B)288
C)120
D)776
E)991
Rationale: Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 10
= 200 m.
Answer:A
Answer: A
Question: he number of sequences in which 9 players can throw a ball, so that the youngest player may not be the last is?
Options:
A)432881
B)322560
C)432020
D)288212
E)278212
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 8 players. The first 8 players can throw the ball in 8p8 ways.
The required number of ways = 8(8!) = 322560
Answer:B
Answer: B
Question: In a sports club with 55 members, 23 play badminton and 29 play tennis and 7 do not play either. How many members play both badminton and tennis?
Options:
A)3
B)5
C)4
D)7
E)8
Rationale: 23+29=52
but where as total number is 55-7=48
therefore answer is 52-48=4
Hence Answer is C
Answer: C
Question: A certain basketball team that has played 2/3 of its games has a record of 15 wins and 5 losses. What is the greatest number of the remaining games that the team can lose and still win at least 3/4 of all of its games?
Options:
A) 7
B) 6
C) 5
D) 4
E) 2
Rationale: 15 wins, 3 losses - total 20 games played.
The team has played 2/3rd of all games so total number of games = 30
3/4th of 30 is 22.5 so the team must win 23 games and can afford to lose at most 7 total games. It has already lost 5 games so it can lose another 2 at most.
Answer (E)
Answer: E
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
Options:
A)Rs.3178
B)Rs.3120
C)Rs.3127
D)Rs.3121
E)Rs.3122
Rationale: Explanation:
Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Answer: B
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)33 1/9%
B)33 8/3%
C)33 1/3%
D)33 2/3%
E)33 1/2%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer: C
Answer: C
Question: A = {2, 3, 4, 5}
B = {4, 5, 6, 7, 8}
Two integers will be randomly selected from the sets above, one integer from set A and one integer from set B. What is the probability M that the sum of the two integers will equal 9 ?
Options:
A) 0.15
B) 0.20
C) 0.25
D) 0.30
E) 0.33
Rationale: Rearrange the first set:
A = {5,4,3,2}
B = {4,5,6,7, 8}
As you can see numbers in each column (the numbers of the same color) give the sum of 9. So there are 4 such pares possible, total # of pairs is 4*5=20.M=favorable/total=4/20=0.2.
Answer: B.
Or: we can select ANY number from set A (4/4=1) but in this case we must select its matching pair from set B (the number of the same color) and since there are only one matching pair of this particular number in B then the probability of this is 1/5. So, overall: M=1*1/5.
Answer: B.
Answer: B