divelab/Sys2Bench huggingface dataset:
Question: A businessman earns $25800 in December, thus decreasing his average annual (January to December) earnings by $1000. His average annual earnings would be
Source: CMAT Preparation
Options:
A)$29000
B)$36800
C)$40200
D)$41000
E)$42300
Rationale: (x - 25,800)/11 - x/12 = 1,000
x = 441,600
x/12 = 36,800
Answer: B
Answer: B
Question: Which of the following data sets has the second smallest standard deviation?
Options:
A) {1, 2, 3, 4, 5}
B) {2, 3, 3, 3, 4}
C) {2, 2, 2, 4, 5}
D) {0, 2, 3, 4, 6}
E) {-1, 1, 3, 5, 7}
Rationale: since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..
The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...
Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..
clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..
Next is D, which has a range of 6-0 or 6..
and has smallest standard of deviation.
and (C) {2, 2, 2, 4, 5} has second smallest standard of deviation.
ans C
Answer: C
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Options:
A)20 hours
B)25 hours
C)35 hours
D)Cannot be determined
E)None of these
Rationale: If c takes x hrs, B takes 2x hrs and A takes 4x hrs,
then
1/x +1/2x = 1/4x = 1/5
7/4x = 1/5
x= 7*5/4 hrs = 35/4 hrs
So A alone will take 4*35/4 = 35 hrs
ANSWER:C
Answer: C
Question: A die is rolled twice. What is the probability of getting a sum equal to 9?
Options:
A)2/9
B)5/7
C)1/7
D)1/9
E)3/7
Rationale: Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces)
Hence, total number of outcomes possible when a die is rolled twice, n(S) = 6 × 6 = 36
E = Getting a sum of 9 when the two dice fall = {(3, 6), {4, 5}, {5, 4}, (6, 3)}
Hence, n(E) = 4
P(E) = n(E)/n(S)
=4/36
=1/9
Answer : Option D
Answer: D
Question: What is the least number which when divided by 8, 12, 15 and 20 leaves in each case a remainder of 5
Options:
A)110
B)125
C)75
D)170
E)195
Rationale: LCM of 8, 12, 15 and 20 = 120
Required Number = 120 + 5 = 125
Answer: Option B
Answer: B
Question: Jane started baby-sitting when she was 18 years old. Whenever she baby-sat for a child, that child was no more than half her age at the time. Jane is currently 32 years old, and she stopped baby-sitting 12 years ago. What is the current age of the oldest person for whom Jane could have baby-sat?
Options:
A)20
B)21
C)22
D)23
E)24
Rationale: Check two extreme cases:
Jane = 18, child = 9, years ago = 32-18 = 14 --> child's age now = 9+14 = 23;
Jane = 20, child = 10, years ago = 32-20 = 12 --> child's age now = 10+12 = 22.
Answer: D.
Answer: D
Question: Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in the train approaching the place hears the second shot 10 minutes after the first. The speed of the trian (in km/hr), supposing that speed travels at 330 metres per second, is:
Options:
A)50.4
B)111.8
C)19.88
D)59.4
E)None
Rationale: Sol.
Let the speed of the train be x m/sec. Then,
Distance travelled by the train in 10 min. = Distance travelled by sound in 30 sec.
∴ Speed of the train = 16.5 m/sec = [16.5*18/5] km/hr = 59.4 km/hr
Answer D
Answer: D
Question: In how many ways can an answer key for a quiz be written if the quiz contains 4 true-false questions followed by 3 multiple-choice questions with 4 answer choices each, if the correct answers to all true-false questions cannot be the same?
Options:
A)512
B)656
C)740
D)896
E)972
Rationale: There are 2^4 = 16 possibilities for the true-false answers.
However we need to remove two cases for TTTT and FFFF.
There are 4*4*4 = 64 possibilities for the multiple choice questions.
The total number of possibilities is 14*64 = 896.
The answer is D.
Answer: D
Question: A train covers a distance of 10 km in 20 min. If it takes 6 sec to pass a telegraph post, then the length of the train is?
Options:
A)50
B)80
C)120
D)100
E)40
Rationale: Speed = (10/20 * 60) km/hr = (30 * 5/18) m/sec = 8.333333 m/sec.
Length of the train = 8.333333 * 6 = 50 m.Answer: A
Answer: A
Question: Simplify (4^y + 4^y + 4^y + 4^y) (4^y + 4^y + 4^y + 4^y)
Options:
A) 4^4y * 3^3y
B) 12^y+1
C) 16^y+1
D) 12^y
E) 4^y * 12^y
Rationale: C
(4^y + 4^y + 4^y + 4^y) (4^y + 4^y + 4^y + 4^y)
(4*4^y)(4*4^y)
16*16^y=16^(y+1)..
Answer: C
Question: If x, y, and z are positive integers such that x is divisible by y, and y is divisible by z, which of the following is NOT necessarily an integer?
Options:
A)xy/z
B)(x + y)/z
C)xz/y
D)(x - y)/z
E)(x + z)/y
Rationale: As per the question, let x = 12, y = 6, and z = 2. Plugging these into the answer choices, only E does not yield an integer. The reason is that (x + z)/y = x/y + z/y, and while x/y must be an integer, z/y is only an integer if y = z.
Answer: E
Question: The average mark of the students of a class in a particular exam is 80. If 5 students whose average mark in that exam is 40 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam?
Options:
A)22
B)26
C)25
D)28
E)12
Rationale: Let the number of students who wrote the exam be x.
Total marks of students = 80 x.
Total marks of (x - 5) students = 90(x - 5)
80x - (5 * 40) = 90(x - 5)
250 = 10x => x = 25
Answer: C
Answer: C
Question: If x and y are perfect squares, then which three of the following is not necessarily a perfect square?
Options:
A)x^2
B)xy
C)4x
D)x+y
E)x^5
Rationale: If x=y=1^2=1, then each option but A is a perfect square, therefore A is NOT necessarily a perfect square.
Answer: A.
Answer: A
Question: Two heavily loaded sixteen-wheeler transport trucks are 787 kilometers apart, sitting at two rest stops on opposite sides of the same highway. Driver A begins heading down the highway driving at an average speed of 90 kilometers per hour. Exactly one hour later, Driver B starts down the highway toward Driver A, maintaining an average speed of 80 kilometers per hour. How many kilometers farther than Driver B, will Driver A have driven when they meet and pass each other on the highway?
Options:
A)90
B)131
C)150
D)320
E)450
Rationale: I've been reading the website for a while and I'm always keen to see different approaches so I would like to share one that works for me:
Short version:
Truck A travels for an hour.
Distance remaining = 787-90 = 697k
Ratio of speeds 9:8 -> 697/17 = 41
Truck A = 90 + 41*9 = 459
Truck B = 41*8 = 328
Delta = 131km
Answer B
Answer: B
Question: A boy goes to his school from his house at a speed of 3 km/hr and returns at a speed of 2 km/hr. If he takes 5 hours in going and coming. The distance between his house and school is?
Options:
A)8 km
B)4 km
C)6 km
D)1 km
E)5 km
Rationale: Average speed = (2 * 3 * 2) / (3 + 2) = 12/5 km/hr.
Distance traveled = 12/5 * 5 = 12 km.
Distance between house and school = 12/2 = 6 km.
Answer: C
Answer: C
Question: John is traveling to a meeting that is 20 miles away. He needs to be there in 30 minutes. How fast does he need to go to make it to the meeting on time?
Options:
A)40 mph
B)37 mph
C)41 mph
D)49 mph
E)56 mph
Rationale: Well 40mph. A. Time*rate=distance --> 0.5*rate=20 --> rate=40
Answer: A
Question: The average of 50 numbers id 38. If two numbers, namely 45 and 55 are discarded, the average of the remaining numbers is :
Options:
A)22.3
B)33.2
C)22.2
D)11.3
E)37.5
Rationale: Explanation:
Total of 50 numbers = (50×38)=1900(50×38)=1900
Total of 48 numbers =(1900-(45+55)]=1800
Required average = 180048=2256=37.5
Answer:E
Answer: E
Question: A, B, C together started a business. A invested Rs.6000 for 5 months B invested Rs.3600 for 6 months and C Rs.7500 for 3 months. If they get a total profit of Rs.7410. Find the share of A?
Options:
A)3098
B)3000
C)2878
D)2899
E)2712
Rationale: 60*5:36*6:75*3
100: 72: 75
100/247 * 7410 = 3000
AnswerB
Answer: B
Question: In the first 20 overs of a cricket game, the run rate was only 4.6. What should be the run rate in the remaining 30 overs to reach the target of 396 runs?
Options:
A)10.13
B)9.13
C)8.13
D)11.13
E)13.13
Rationale: Required run rate = 396 - (4.6 x 20)	/30	=	304/30 = 10.13 Option A
Answer: A
Question: What will be the vulgar fraction of 0.60
Options:
A)3/7
B)3/5
C)3/2
D)3/7
E)3/8
Rationale: Explanation:
0.6 = 60/100 = 3/5
Option B
Answer: B
Question: A train 130 meters long takes 6 seconds to cross a man walking at 5 kmph in the direction opposite to that of the train. Find the speed of the train.
Options:
A)45 kmph
B)50 kmph
C)55 kmph
D)60 kmph
E)73 kmph
Rationale: Explanation:
Let the speed of the train be x kmph.
Speed of the train relative to man = (x + 5) kmph = (x + 5) ×5/18 m/sec.
Therefore 130/((x+5)×5/18)=6 <=> 30 (x + 5) = 2340 <=> x = 73
Speed of the train is 73 kmph.
Answer: Option E
Answer: E
Question: which of the following options is a multiple of 5!-20?
Options:
A)4!+76
B)5!+80
C)4!-10
D)5!+10
E)2!+6
Rationale: The factorial 5! is same as 5*4*3*2
Therefore 5!-20 =(5*4*3*2)-20
This gives you 120-20=100
A is the correct option.
Answer: A
Question: If r > a and L < a, which of the following cannot be true?
Options:
A) d + L = 14
B) d - L = 7
C) d - L = 1
D) a - r = 9
E) a + d = 9
Rationale: Is the answer D?
If r>a, then r-a>0 (always positive). The converse would be a-r<0 (always negative). Option D states that a-r=9, which can never be true.
Answer: D
Question: If 5 is one solution of the equation x^2 + 3x + k = 10, where k is a constant, what is the other solution?
Options:
A) -8
B) -4
C) -3
D) 1
E) 6
Rationale: The phrase “5 is one solution of the equation” means that one value of x is 5. Thus, we first must plug 5 for x into the given equation to determine the value of k. So we have
5^2 + (3)(5) + k = 10
25 + 15 + k = 10
40 + k = 10
k = -30
Next we plug -30 into the given equation for k and then solve for x.
x^2 + 3x – 30 = 10
x^2 + 3x – 40 = 0
(x+8)(x-5) = 0
x = -8 or x = 5
Thus, -8 is the other solution. Answer A.
Answer: A
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 16% less than the price each head sold for the day before.what was the gross profit on this shipment?
Options:
A)$100
B)$110
C)$125
D)$130
E)$135
Rationale: Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 84% of the previous price: 84/100 * 1/2 = $(21/50)
Total revenue by selling 500 heads = 21/50 * 500 = 210
Total revenue after selling 1500 cabbage heads - 210+500 = $710
Money spent on the purchase: $600
Profit = 710-600 = $110
Ans: B
Answer: B
Question: A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum?
Options:
A)7500
B)7522
C)2789
D)3677
E)2793
Rationale: P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8
= Rs.7500
Answer:A
Answer: A
Question: A number of cats got together and decided to kill between them 999919 mice. Every cat killed an equal number of mice. Each cat killed more mice than there were cats. How many cats do you think there were?
Options:
A)1009
B)1110
C)1111
D)1112
E)1122
Rationale: 999919 = 1000000 - 81 = 1000^2 - 9^2 = (1000+9)(1000-9) = 1009*991.
Since there were more mice than there were cats, 991 cats killed 1009 mice each.
ANSWER:A
Answer: A
Question: A student is ranked 13th from right and 8th from left. How many students are there in totality ?
Options:
A)18
B)19
C)20
D)21
E)22
Rationale: From right 13 , From left 8
Total = 13+8-1 = 20
ANSWER:C
Answer: C
Question: A batsman scored 120 runs whichincluded 3 boundaries and 8sixes. What % of his total score did he make by running between the wickets
Options:
A)40 %
B)50 %
C)60 %
D)70 %
E)80 %
Rationale: Number of runs made by running = 110 - (3 x 4 + 8 x 6)
= 120 - (60)
= 60
Now, we need to calculate 60 is what percent of 120.
=> 60/120 * 100 = 50 %
B
Answer: B
Question: In a group of 100 adults, 60 percent of the women are left-handed. If there are 12 right-handed women in the group, how many men are in the group?
Options:
A)40
B)52
C)54
D)60
E)62
Rationale: 12 left-haded women compose 100-60=40% (or 2/5) of all women, so there are total of 5*12=60 women --> 100-60=40 men.
Answer: A.
Answer: A
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 2?
Options:
A)$0.50
B)$0.75
C)$1.25
D)$1.50
E)$1.75
Rationale: Salary grade of 5 is p(5)=9.50+0.25(5–1)=9.50+0.25*4;
Salary grade of 2 is p(2)=9.50 + 0.25(2–1)=9.50+0.25;
p(5)-p(2)=9.50+0.25*4-9.50-0.25=0.75.
Answer: B.
Answer: B
Question: There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 45% play football, how many play both?
Options:
A)120
B)150
C)200
D)180
E)160
Rationale: n(A) = 75*600/100 = 450
n(B) = 45*600/100 = 270
n(AUB) = 600
n(AnB) = 450+270-600 = 120
Answer is A
Answer: A
Question: Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio A of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job?
Options:
A)5 to 1
B)10 to 7
C)1 to 5
D)7 to 10
E)9 to 10
Rationale: Solutioning this exercise can be facilitated by using a R T W (rate time work) table:
We translate the exercise into the table:
R T W
X t/2 1
Y t 1
Z (t/2*3/2 =3t/4) 1
From this table we find the rates
Rx = 2/t
Ry = 1/t
Rz = 4/3t
The Q is what is the ratio of (Tx + Ty) / (Ty + Tz)
Rx + Ry = 2/t + 4/3t = 6/3t+4/3t = 10/3t
Ry+Rz = 1/t + 4/3t = 3/3t + 4/3t = 7/3t
The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7
Since Time Ratio A is the inverse of work, the the answer is 7 to 10
CORRECT ANSWER D
Answer: D
Question: An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest after one year becomes:
Options:
A)10.25%
B)10.5%
C)10.75%
D)10%
E)None of these
Rationale: Explanation :
Let the automobile financier lends Rs.100
Simple Interest for first 6 months = PRT/100=100×10×12/100=Rs. 5
After 6 months, he adds the simple interest to principal
i.e., after 6 months, principal becomes Rs.100 + Rs.5 = Rs.105
Simple Interest for next 6 months = PRT/100=105×10×1/2 /100=Rs. 5.25
Amount at the end of 1 year = Rs.105 + Rs. 5.25 = Rs.110.25
i.e., Effective Simple Interest he gets for Rs.100 for 1 year = 110.25 - 100 = 10.25
i.e, the Effective Rate of Interest = 10.25%
(∵R = 100×SI/PT=100×10.25/100×1=10.25%)
Answer : Option A
Answer: A
Question: What percent of the different arrangements of the letters of the word ADACUS are those in which the vowels appear together?
Options:
A)20%
B)25%
C)30%
D)40%
E)50%
Rationale: let's determine the number of total possibilities in arranging the letters. There are six spaces, so the total number of arrangements is 6!, or 360.
Next, we need to figure out how to determine the number of ways that we can arrange the 3 vowels together - simply place them together (as in AAU) and call that a single place.
Next, we must determine the number of ways to arrange the now 4 units (i.e., AAU, B, C, S). Like above, there are 4 units and 4 places so the number of arrangements is 4!, or 24.
Finally, we need to account for the number of ways we can arrange AAU. We can either write out each unique iteration (AAU, AUA and UAA) or calculate as 3!/2! and get 3.
Putting this all together, we get the number of ways to arrange the letters so that the vowels are together is 4! x 3 ==> 72
the number of total arrangements of all the letters is 6! ==> 360
72/360 = 1/5, or 20%
Correct answer is A
Answer: A
Question: Which digits should come in place of * and $ if the number 62684*$ is divisible by both 8 and 5 ?
Options:
A)8,5
B)4,0
C)1,4
D)0,8
E)8,0
Rationale: Since the given number is divisible by 5, so 0 or 5 must come in place of $. But, a number ending with 5 is never divisible by 8. So, 0 will replace $.
Now, the number formed by the last three digits is 4*0, which becomes divisible by 8, if * is replaced by 4.
Hence, digits in place of * and $ are 4 and 0 respectively.
ANSWER B 4,0
Answer: B
Question: If a and b are even numbers, which of the following CANNOT be the value of ab?
Options:
A)6
B)14
C)21
D)24
E)26
Rationale: 21 is a odd number. The multiple of two even number should be an even number
ans C
Answer: C
Question: A man in train notice that he can count 51 telephone posts in 1 minute. If they are known to be 60 meters apart,then at what speed is the train traveling?
Options:
A)100km/hr
B)110km/hr
C)50km/hr
D)180km/hr
E)200km/hr
Rationale: Number of gaps between 51 telephone posts = 50
Distance traveled in 1 minute = 50*60 = 3000m = 3km
Speed = 60*3=180km/hr
Answer is D
Answer: D
Question: A train 200 m long running at 80 kmph crosses a platform in 22 sec. What is the length of the platform?
Options:
A)338
B)277
C)350
D)288
E)271
Rationale: D = 80 * 5/18 = 22 = 488 – 200 = 288
Answer: D
Answer: D
Question: Present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. What is father's present age?
Options:
A)30
B)31
C)33
D)35
E)37
Rationale: Let the present age the son =x
Then, present age of the father =3x+3
Given that, three years hence, father's age will be 10 years more than twice the age of the son
⇒(3x+3+3)=2(x+3)+10⇒x=10
Father's present age
=3x+3=3×10+3=33
Answer is B.
Answer: B
Question: A man walks at a speed of 2 km/hr and runs at a speed of 6 km/hr. How much time will the man require to cover a distance of 20 1/2 km, if he completes half of the distance, i.e., (10 1/4) km on foot and the other half by running ?
Options:
A)41.9 hrs
B)11.9 hrs
C)61.9 hrs
D)17.9 hrs
E)71.9 hrs
Rationale: Explanation:
We know that
Time = Distance/speed
Required time = (10 1/4)/2 + (10 1/4)/6
= 41/8 + 41/6
= 287/24 = 11.9 hours.
Answer: B
Answer: B
Question: A goods truck travels from a place at a certain time and at fixed speed. After 6hrs another truck leaves the same place and move in same direction of uniform speed of 90kmph. The truck catches up the goods truck in 4hrs. Find the speed of the goods truck ?
Options:
A)36 kmph
B)86 kmph
C)66 kmph
D)26 kmph
E)62 kmph
Rationale: Explanation:
Let the speed of goods truck be 'p' kmph
Distance covered by goods truck in 10hrs (4+6) = Distance covered by other truck in 4 hrs.
10p = 4 x 90
p = 36kmph.
Therefore, the speed of the goods truck is p = 36 kmph.
Answer: A
Answer: A
Question: Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: If 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys
49 - 5 = 44 for Tom and Bob
If distributed equally, each one will have
44 / 2 = 22 toys
Bob has 5 more toys than Tom, so Bob has
22 + 5 = 27 toys
correct answer C
Answer: C
Question: In a goat farm, the goat give birth to lamps and the count of goat increases by 60% every year. How many years it will take to get the count tripled?
Options:
A)270
B)780
C)209
D)790
E)488.28
Rationale: 1 year: 100/4 = 60 : Total: 160
2nd year: 160/4 = 40: Total: 160+40= 200
3rd year: 200/4 = 50 approx: Total: 200+50 = 250
4th year:250/4 = 62.5: Total: 250+62.5= 312.5
5th year : 312.5/4 = 78.125: total : 312.5+78.125 = 390.63
6th year : 390.63/4 = 97.65 : total : 390.63+97.65 = 488.28
;6 years;
ANSWER: E
Answer: E
Question: The average of 45 results is 9. The average of first 22 of them is 15 and that of last 22 is 20. Find the 23 result?
Options:
A)515
B)480
C)750
D)650
E)560
Rationale: 23th result = sum of 45results - sum of 44 results
9*45-15*22+20*22 = 450-330+440 = 515
Answer is A
Answer: A
Question: Among all sales staff at Amtek Corporation, college graduates and those without college degrees are equally represented . Each sales staff member is either a level-1 or level-2 employee. Level-1 college graduates account for 15% of Amtek's sales staff. Amtek employs 80 level-1 employees, 30 of whom are college graduates. How many sales staff members without college degrees are level-2 employees ?
Options:
A)46
B)42
C)50
D)32
E)58
Rationale: I'm going in on this one.
So let's say that we have the following
So we know that L1 = 80 and that C and L1 = 0.15X , we should set up a double set matrix btw but anyways, I'm just explaining the point with this problem. Now we are told that 0.15x = 30, therefore the grand total is 200. Now we know that L2 is 200 - 80 = 120. We also learn that C and No C are equally represented thus 100 each. Therefore No C and No L2 will be 100 - 50 = 50.
Thus C is the correct answer choice
Answer: C
Question: A particular parking garage is increasing its rates by 20 percent per month. Bob decides to reduce the number of days he uses the garage per month so that the amount he spends at the garage per month remains unchanged. Which of the following is closest to Bob’s percentage reduction in the number of days he uses the garage each month?
Options:
A)10%
B)12%
C)15%
D)17%
E)20%
Rationale: Let x be the original number of days that Bob used the garage.
Let P be the original cost per day.
Let N*x be the new number of days that Bob uses the garage.
N*x*1.2P = x*P
N*x = x/1.2 which is about 0.83x, thus a 17% reduction.
The answer is D.
Answer: D
Question: If x and y are positive integers such that (3x+7y) is a multiple of 11, then which of the followings are divisible by 11?
Options:
A)9x+4y
B)x+y+4
C)4x-9y
D)4x+6y
E)5x+3y
Rationale: By hit and trial method, we get
x=5 and y=1 such that
3x+7y=15+7=22 is a multiple of 11.
(4x+6y)=(4×5+6×1)=26
=> not divisible by 11
(x+y+4)=(5+1+4)=10
=> not divisible by 11
(9x+4y)=(9×5+4×1)=49
=> not divisible by 11
(4x−9y)=(4×5−9×1)=20−9=11
=> divisible by 11
Answer : C
Answer: C
Question: A store reported total sales of $460 million for February of this year. If the total sales for the same month last year was $320 million, approximately what was the percent increase in sales?
Options:
A)2%
B)17%
C)44%
D)65%
E)83%
Rationale: New Value – Old Value)/Old Value x 100
We are given:
February sales this year = 460 million
February sales last year = 320 million
We need to determine the percent increase between sales from last year to sales this year.
Thus, the new value = 460 million and the old value = 320 million. Let’s plug them into our percent change formula.
(New Value – Old Value)/Old Value x 100
[(460 – 320)/320] x 100
≈ 44%.
The answer is C.
Answer: C
Question: What is the smallest number which when diminished by 18, is divisible 8, 14, 26 and 28?
Options:
A)746
B)750
C)789
D)678
E)897
Rationale: Required Number
= (LCM of 8, 14, 26 and 28) + 18
= 728 + 18 = 746
Option A
Answer: A
Question: A company recently conducted a survey and found that 35,000 of its customers live in rural areas. If the number of customers who live in urban areas is 140 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?
Options:
A)78,000
B)80,000
C)82,000
D)84,000
E)86,000
Rationale: The number of customers in urban areas is 35,000+1.4*35,000=84,000.
The answer is D.
Answer: D
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning?
Options:
A)40
B)56
C)39
D)42
E)53
Rationale: Let the average after 7th inning = x Then average after 16th inning = x - 3 therefore 16(x-3)+87 = 17x therefore x = 87 - 48 = 39 Answer : C
Answer: C