mathewhe/aqua_rat huggingface dataset:
Question: Using only the digits from 0 to 6 , how many 5 digit codes can be constructed, if the first digit can not be 4 and no digits is used more than once ?
(A) 1080
(B) 2160
(C) 777
(D) 720
(E) 620
Rationale: code can be contain zero,(ex 0122---, 0731---)
sw, we can consider 0 at first place.
so it should be 6*6*5*4*3= 2160
ANSWER:B
Answer: (B) 2160
Question: A, Band C can do a piece of work in 11 days, 20 days and 55 days respectively, working alone. How soon can the work be done if A is assisted by Band C on alternate days?
(A) 7 days
(B) 8 days
(C) 9 days
(D) 10 days
(E) 11 days
Rationale: (A+B)'s 1 day's work = 1/11+1/20 = 31/220
(A+C)'s 1 day's work = 1/11+1/55 = 6/55
work done in 2 day's = 31/220+6/55 = 55/220 = 1/4
1/4th work done in 2 days
work done= 4*2 = 8 days
ANSWER:B
Answer: (B) 8 days
Question: L is a positive integer and 225 and 216 are both divisors of L. If L=(2^a)*(3^b)*(5^c), where a, b and c are positive integers, what is the least possible value of a+ b+ c?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 7
Rationale: Lets make factorization of 225 and 216 ..
225 = 5 X 5 X 3 X 3 X 3
216 = 2 X 2 X 2 X 3 X 3 X 3
L would have to have 3 two's , 225 has 3 threes and and so does 216 but they can be the same three threes so we count them only once ... 225 has 2 fives ... So we had them together and we get 3 + 3 + 2 = 8(D) (answer) ...
Answer: (D) 8
Question: The ratio between the length and the breadth of a rectangular park is 3 : 2. If a man cycling alongthe oundary of the park at the speed of 12 km/hr completes one round in 8 min, then the area of the park (in sq. m) is?
(A) 123600 m
(B) 141600 m
(C) 153600 m
(D) 161600 m
(E) 165600 m
Rationale: Perimeter = Distance covered in 8 min. = 12000 x 8 m = 1600 m.
60
Let length = 3x metres and breadth = 2x metres.
Then, 2(3x + 2x) = 1600 or x = 160.
Length = 480 m and Breadth = 320 m.
Area = (480 x 320) m2 = 153600 m
C
Answer: (C) 153600 m
Question: If a and b are each greater than x and y, which of the following must be true?
I. ab > xy
II. |a| + |b| > |x| + |y|
III.a + b > x + y
(A) I only
(B) II only
(C) I and II
(D) I and III
(E) I, II and III
Rationale: I. a + b > x + y. Since a and b are each greater than x and y, then the sum of a and b will also be greater than the sum of x and y.
II. ab > xy. Not necessarily true, consider a = b = 0 and x = y = -1 --> ab = 0 < 1 = xy.
III. |a| + |b| > |x| + |y|. Not necessarily true, consider a = b = 0 and x = y = -1 --> |a| + |b| = 0 < 2 = |x| + |y|.
Answer: B.
Answer: (B) II only
Question: If a boat goes 5 km upstream in 50 minutes and the speed of the stream is 3 kmph, then the speed of
the boat in still water is
(A) 9 kmph
(B) 13 kmph
(C) 14 kmph
(D) 15 kmph
(E) None of these
Rationale: Explanation:
Rate upstream = (5/50)*60 kmh = 6 kmph.
Speed of stream = 3 kmph.
Let speed in still water is x km/hr
Then, speed upstream = (x ï¿½3) km/hr.
x-3 = 6 or x = 9 kmph
Answer: A
Answer: (A) 9 kmph
Question: The expression ab+a is odd when the a and b are integers. Which of the following expressions must be even?
(A) a
(B) b
(C) a + b
(D) ab - a
(E) a + b^2
Rationale: ab+a is odd
a and b are integers
If a were even "ab+a" would be even despite any value of b.
B can't be odd, so "b" must be even.
Ans : B
Answer: (B) b
Question: The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles?
(A) 1987 sq m
(B) 7867 sq m
(C) 1897 sq m
(D) 4783 sq m
(E) 4312 sq m
Rationale: Let the radii of the smaller and the larger circles be s m and l m respectively.
2∏s = 264 and 2∏l = 352
s = 264/2∏ and l = 352/2∏
Difference between the areas = ∏l2 - ∏s2
= ∏{1762/∏2 - 1322/∏2}
= 1762/∏ - 1322/∏
= (176 - 132)(176 + 132)/∏
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m
Answer:E
Answer: (E) 4312 sq m
Question: If the letters of the word PLACE are arranged taken all at a time, find how many do not start with AE
(A) 110
(B) 112
(C) 114
(D) 118
(E) 120
Rationale: Total no'of arrangements 5P5 = 5! = 120
no'of arrangements start with AE = 1 × 6 = 6
no'of arrangements which do not start with AE = 120 - 6 = 114.
C
Answer: (C) 114
Question: What is the difference between the C.I. on Rs. 8000 for 1 1/2 years at 4% per annum compounded yearly and half-yearly?
(A) s.3.26
(B) s.2.08
(C) s.2.02
(D) s.2.83
(E) s.2.42
Rationale: C.I. when interest is compounded yearly
= [8000 * (1 + 4/100) * (1 + (1/2 * 4)/100]
= 8000 * 26/25 * 51/50 = Rs. 8486.4
C.I. when interest is compounded half-yearly
= [8000 * (1 + 2/100)2]
= (8000 * 51/50 * 51/50 * 51/50)
= Rs. 8489.66 Difference
= (8489.66 - 8486.4
= Rs.3.26.
Answer: A
Answer: (A) s.3.26
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum V of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
(A) 6x
(B) V=4x
(C) V=5x/3
(D) 3x/2
(E) 3x/5
Rationale: OA please. Yeah so 5x is the sum of the 5, then I guess 4x could be the answer (B)
But what about C,D,E? Any ideas why these could be wrong?
Note that we have 5positivetemperatures.
Next, as the average is x then the sum of the temperatures is 5x and as all the temperatures are positive then the sum of the 3 greatest must be more than (or equal to) 3x (as the average of the 3 greatest must be at least x) and less than 5x: 3x<SUM<5x --> only option B fits.
Answer: B.
Answer: (B) V=4x
Question: A water tank is two-fifth full. Pipe A can fill a tank in 10 minutes and pipe B can empty it in 6 minutes. If both the pipes are open, how long will it take to empty or fill the tank completely?
(A) 6
(B) 7
(C) 8
(D) 5
(E) 3
Rationale: Clearly, pipe B is faster than pipe A and so, the tank will be emptied.
Part to be emptied = 2/5
Part emptied by (A + B) in 1 minute = (1/6 - 1/10) = 1/15
1/15 : 2/5 :: 1 : x
x = (2/5 * 1 * 15) = 6 min.
So, the tank will be emptied in 6 min. Answer: A
Answer: (A) 6
Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 4 or 15 ?
(A) 9/10
(B) 6/10
(C) 2/10
(D) 3/10
(E) 5/10
Rationale: Explanation:
Here, S = {1, 2, 3, 4, ...., 19, 20}=> n(s) = 20
Let E = event of getting a multiple of 4 or 15
=multiples od 4 are {4, 8, 12, 16, 20}
And multiples of 15 means multiples of 3 and 5
= {3, 6 , 9, 12, 15, 18, 5, 10, 15, 20}.
= the common multiple is only (15).
=> E = n(E)= 6
Required Probability = P(E) = n(E)/n(S) = 6/20 = 3/10.
Answer is D
Answer: (D) 3/10
Question: There are 2 couples. If they will sit 4 chairs in a row such that each couple sits side by side, how many possible cases are there?
(A) 120
(B) 8
(C) 1,200
(D) 2,460
(E) 3,840
Rationale: Tie the couples. Then we have 2 persons that have to be arranged in 2 places. 2! ways.
Now the couples can change position with each other. 2! ways.
2! * (2!)^2 = 2 *4 = 8
Answer is B.
Answer: (B) 8
Question: A bus started its journey from Mumbai and reached Pune in 44min with its average speed of 50 km/hr. If the average speed of the bus is increased by 5km/hr, how much time will it take to cover the same distance?
(A) 10 min
(B) 20 min
(C) 30 min
(D) 40 min
(E) 60 min
Rationale: Sol. Distance between Ramgarh and Devgarh =(50*44)/60=110/3
Average speed of the bus is increased by 5 km/hr then the
speed of the bus = 55 km/hr
Required time = 110/3*60/55 = 40 min
D
Answer: (D) 40 min
Question: A man can row 7.5 kmph in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of stream.
(A) 2.5 km/hr
(B) 12.5 km/hr
(C) 1 2.6 km/hr
(D) 22.5 km/hr
(E) 22.6 km/hr
Rationale: Given that, time taken to travel upstream = 2 × time taken to travel downstream
When distance is constant, speed is inversely proportional to the time
Hence, 2 × speed upstream = speed downstream
Let speed upstream = x
Then speed downstream = 2x
we have, 1/2(x+2x) = speed in still water
⇒1/2(3x)=7.5
3x = 15
x = 5
i.e., speed upstream = 5 km/hr
Rate of stream = 1/2(2x−x)=x/2=5/2=2.5 km/hr
Answer is A
Answer: (A) 2.5 km/hr
Question: The New York Classical Group is designing the liner notes for an upcoming CD release. There are 10 soloists featured on the album, but the liner notes are only 5 pages long, and therefore only have room for 5 of the soloists. The soloists are fighting over which of them will appear in the liner notes, though not about which page they appear on. How many different combinations Q of soloists can appear in the liner notes?
(A) 5!
(B) 10!/(5!5!)
(C) 10!/5!
(D) 10!
(E) 10!*5!
Rationale: Total Soloists to choose from = 10
Soloist Required = 5
Question : How many different combinations Q of soloists can appear in the liner notes?
The language of the question clearly mentions that only the combinations need to be calculated
i.e. Arrangement of the Soloists does NOT matter(Refer theHighlightedpart of the question)
Method-1:
Total Ways to Choose 5 out of 10 soloists = 10C5 = 10! / (5!*5!)
Method-2:
No. of ways to select and arrange 5 soloist on 5 Page = 10*9*8*7*6
Since the arrangement of 5 selected Notes (which can happen in 5! ways) doesn't NOT matter,
Therefore total ways to pick 5 out of 10 soloists = 10*9*8*7*6 / 5! = 10*9*8*7*6 *5! / (5!*5!) = 10! / (5!*5!)
Answer: Option B
Answer: (B) 10!/(5!5!)
Question: What is the place value of 0 in the numeral 2074?
(A) 0
(B) 1
(C) 2
(D) 5
(E) 6
Rationale: Note : The place value of zero (0) is always 0. It may hold any place in a number,
its value is always 0.
A
Answer: (A) 0
Question: A boat running downstream cover a distance of 24km in 6 hr while covering the same distance upstream it takes 8 hr then the speed of the boat still in the water
(A) 4.5km/hr
(B) 9.5km/hr
(C) 3.5km/hr
(D) 25.6km/hr
(E) 12.3km/hr
Rationale: rate down stream=(24/6)= 4kmph
rate upstream=(24/8)= 3kmph
speed still water =1/2(4+3)kmph=3.5km/hr
Answer(C)
Answer: (C) 3.5km/hr
Question: The cost to rent a small bus for a trip is x dollars, which is to be shared equally among the people taking the trip. If 10 people take the trip rather than 12, how many more dollars, in terms of x, will it cost per person?
(A)  x/6
(B)  x/16
(C)  x/40
(D)  3x/40
(E)  3x/80
Rationale: Choose x as a multiple of 16, I chose 64:
So for 10 people, that's 6.4 each and for 12 people it's 4 USD each... Pick one of the options that gives you 6.4 - 4 = 2.4... The answer is C.
Answer: (C)  x/40
Question: A grocer has a sale of Rs. 4435, Rs. 4927, Rs. 4855, Rs. 5230 and Rs. 4562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 4500?
(A) 1991
(B) 2991
(C) 3991
(D) 4521
(E) 5991
Rationale: Total sale for 5 months = Rs. (4435 + 4927 + 4855 + 5230 + 4562) = Rs. 24009.
Required sale = Rs. [ (4500 x 6) - 24009 ]
= Rs. (27000 - 24009)
= Rs. 2991
Answer: Option B
Answer: (B) 2991
Question: On a game show, a contestant is given three keys, each of which opens exactly one of three identical boxes. The first box contains $5, the second $500, and the third $5000. The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. What is the probability that a contestant will win more than $5000?
(A) 1/9
(B) 4/6
(C) 3/6
(D) 1/2
(E) 1/6
Rationale: Let's call the boxes that contain $5, $500, and $5000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.
We want to know the probability of winning more than $5000. Notice that if the distribution of keys is:
Box A = Key B
Box B = Key A
Box C = Key C
then the contestant wins exactly $5000, not more than $5000. The only configuration that leads to winning more than $1000 is:
Box A = Key A
Box B = Key B
Box C = Key C
i.e., getting all three keys correct. That's the only way to be more than $5000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?
Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.
Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is
Probability = 1/6
Answer: E
Answer: (E) 1/6
Question: Working simultaneously and independently at an identical constant rate, 30 machines of a certain type can produce a total of x units of product P in 3 days. How many of these machines, working simultaneously and independently at this constant rate, can produce a total of 5x units of product P in 10 days?
(A) 41
(B) 44
(C) 45
(D) 47
(E) 50
Rationale: The rate of 30 machines is rate=job/time=x/3 units per day --> the rate of 1 machine 1/30*(x/3)=x/90 units per day;
Now, again as {time}*{combined rate}={job done}
then 10*(m*x/90)=5x --> m=45.
Answer: C.
Answer: (C) 45
Question: Five different books (A, B, C, D and E) are to be arranged on a shelf. Books A , B ,C and D ARE to be arranged first and second starting from the right of the shelf. The number of different orders in which books E may be arranged is
(A) 5!
(B) 6!
(C) 8!
(D) 1!
(E) 12!
Rationale: Solution
Since books A, B,C and D is arranged first and second, only book E will change order. Therefore it an arrangement problem involving 1 items and the number of different order is given by
1!
Answer D
Answer: (D) 1!
Question: In how many ways can 7 distinct objects be divided among three people so that either one or two of them do not get any object?
(A) 281
(B) 304
(C) 316
(D) 381
(E) 391
Rationale: Case 1: Two guys don't get anything. All items go to 1 person. Hence, 3 ways.
Case 2: 1 guy doesn't get anything. Division of 7 items among 2 guys. Lets say they are called A & B.
a) A gets 6. B gets 1. 7 ways.
b) A gets 5. B gets 2. 21 ways.
c) A gets 4. B gets 3. 35 ways.
d) A gets 3. B gets 4. 35 ways.
e) A gets 2. B gets 5. 21 ways.
f) A gets 1. B gets 6. 7 ways.
Total = 126 ways to divide 7 items between A & B.
Total number of ways for case 2 = 126*3 = 378 (Either A, or B, or C don't get anything).
Answer = Case 1 + Case 2 = 3 + 378 = 381
ANSWER:D
Answer: (D) 381
Question: A basket has 5 apples and 4 oranges. Three fruits are picked at random. The probability that at least 2 apples are picked is ?
(A) 27/42
(B) 25/499
(C) 25/45
(D) 25/41
(E) 25/42
Rationale: Total fruits = 9
Since there must be at least two apples,
= 25/42.
Answer: A
Answer: (A) 27/42
Question: A dishonest dealer professes to sell goods at the cost price but uses a weight of 800 grams per kg, what is his percent?
(A) 15%
(B) 25%
(C) 65%
(D) 45%
(E) 35%
Rationale: Explanation:
800 --- 200
100 --- ? => 25%
Answer: B
Answer: (B) 25%
Question: X and Y are two points respectively on sides AB and AC of triangle ABC such that XY is parallel to BC. If the ratio of area of triangle AXY to that of the trapezium XYCB is 25:144 and XY=13 cm, then find the length of BC.
(A) 12
(B) 13
(C) 14
(D) 11
(E) 15
Rationale: ABC and AXY are similar triangles.
So (side of ABC/side of AXY)^2=169/25
side of ABC/side of AXY = 13/5
So the length of BC = 5
Answer - D
Answer: (D) 11
Question: 8 couples (husband and wife) attend a dance show "Nach Baliye' in a popular TV channel ; A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is atleast one couple will be selected is :
(A) 15/38
(B) 15/39
(C) 15/31
(D) 15/32
(E) 15/34
Rationale: Explanation:
P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)
=
Answer: B) 15/39
Answer: (B) 15/39
Question: Look at this series: 0.25, 1.75, ____, 85.75, 600.25, ... What number should fill the blank?
(A) 11.25
(B) 12.25
(C) 13.25
(D) 9.25
(E) 10.75
Rationale: This is a simple multiplication series. Each number is 7 times greater than the previous number.
Answer: B
Answer: (B) 12.25
Question: In how many years does a sum of Rs. 5000 yield a simple interest of Rs. 16500 at 15% p.a.?
(A) 22 years
(B) 67 years
(C) 88 years
(D) 55 years
(E) 33 years
Rationale: T = (100 * 16500)/(15 * 5000) = 22 years.Answer: A
Answer: (A) 22 years
Question: How many even number in the range between 10 to 170 inclusive are not divisible by 3
(A) 15
(B) 30
(C) 31
(D) 33
(E) 54
Rationale: We have to find the number of terms that are divisible by 2 but not by 6( as the question asks for the even numbers only which are not divisible by 3)
For 2,
10,12,14...170
using AP formula, we can say 170 = 10 + (n-1) *2
or n=81.
For 6,
12,18,...168
using AP formula, we can say 168 = 12 + (n-1) *6
or n=27.
Hence, only divisible by 2 but not 3 = 81-27 = 54. hence, Answer E
Answer: (E) 54
Question: Find the mean proportional between 49 & 64?
(A) A)59
(B) B)61
(C) C)56
(D) D)65
(E) E)67
Rationale: Formula = √a×b
A = 49 and B = 64
√49×64 = 7 × 8 = 56
C
Answer: (C) C)56
Question: The sum of all the integers a such that -26 < a < 24 is
(A) 0
(B) -2
(C) -25
(D) -49
(E) -51
Rationale: Easy one -
-25, -24, -23,-22,...... -1,0, 1, 2...., 22, 23
Cancel everyhitng and we're left with - -25 and -24 a = -49.
D is the answer.
Answer: (D) -49
Question: A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. working together, they can do it in
(A) 20 days
(B) 22 ½ days
(C) 25 days
(D) 30 days
(E) 35 days
Rationale: Explanation:
B = 3A
3A – A =60 days
A = 30days
Then, B = 90 days
(A + B) = 30 × 90/ 120 = 45/2 = 22 ½ days .
Answer: Option B
Answer: (B) 22 ½ days
Question: After taking N tests, each containing 100 questions, John had an average of 70% of correct answers. How much does John need to score on the next test to make his average equal 70%?
M13-03.
(A) N−35
(B) N+69
(C) 2N+70
(D) 2N+72
(E) 2N−35
Rationale: Say N=1.
So, after 1 test John has 70 correct answers.
In 2 tests, so in 200 questions he needs to have 0.70*200=140 correct answers, so in the second test he must get 140-70=70 questions correctly.
Now, plug N=1 into the answer choices to see which one yields 70. Only option D fits.
Answer: B.
Answer: (B) N+69
Question: If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many C such committees are possible?
(A) 20
(B) 40
(C) C=50
(D) C=80
(E) C=120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: (D) C=80
Question: If a sample of data has mean of 20 and SD of 3, which of the following values is more than 2.6 SDs from the mean?
(A) 13
(B) 14
(C) 12
(D) 15
(E) 16
Rationale: 2.6 SD's mean is equal to: +/- 2.6*3 = +/- 7.8
ie. 12.2 to 27.8
Answer is: C
Answer: (C) 12
Question: Calculate the cost of j bottles of wine given that the cost of k bottles of said wine is c rupees?
(A) Rs.(c*k)
(B) Rs.(j*k)
(C) Rs.(j-k)
(D) Rs.(c/k)
(E) Rs.(jc/k)
Rationale: Cost of k bottles = Rs. c.
Cost of 1 bottle = Rs.	c/k
Cost of j bottles = Rs.(c/k)* j= Rs.(jc/k)
Answer is E.
Answer: (E) Rs.(jc/k)
Question: The average of 21 numbers is 44. Average of the first 11 of them is 48 and that of the last 11 is 41. Find the 11th number?
(A) 48
(B) 51
(C) 47
(D) 49
(E) 55
Rationale: Sum of all the 21 numbers = 21 * 44 = 924Sum of the first 11 of them = 11 * 48 = 528Sum of the last 11 of them = 11 * 41 = 451So, the 11th number = 528 + 451 - 924= 55.Answer: E
Answer: (E) 55
Question: If,
1 * 3 * 5 = 16
3 * 5 * 7 = 38
Then find,
5 * 7 * 9 =?
(A) 65
(B) 68
(C) 72
(D) 80
(E) 77
Rationale: B
68
(9 * 7) + 5 = 68
Answer: (B) 68
Question: A boat goes 100 km downstream in 10 hours, and 75 m upstream in 15 hours. The speed of the stream is?
(A) 2 9 ½ kmph
(B) 8 2 ½ kmph
(C) 2 7 ½ kmph
(D) 2 2 ½ kmph
(E) 3 2 ½ kmph
Rationale: 100 --- 10 DS = 10
? ---- 1
75 ---- 15 US = 5
? ----- 1 S = (10 - 5)/2
= 2 2 ½ kmph
Answer: D
Answer: (D) 2 2 ½ kmph
Question: Laxmi and Prasanna set on a journey. Laxmi moves northwards at a speed of 15 kmph and Prasanna moves southward at a speed of 45 kmph. How far will be Prasanna from Laxmi after 60 minutes ?
(A) 11
(B) 50
(C) 28
(D) 27
(E) 60
Rationale: Explanation:
We know 60 min = 1 hr
Total northward Laxmi's distance = 15 kmph x 1hr = 15 km
Total southward Prasanna's distance = 45 kmph x 1hr = 45 km
Total distance between Prasanna and Laxmi is = 15 + 45 = 60 km.
Answer: E
Answer: (E) 60
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
(A) 106 kmph
(B) 104 kmph
(C) 114 kmph
(D) 108 kmph
(E) 110 kmph
Rationale: B
104 kmph
624/6 = 104 kmph
Answer: (B) 104 kmph
Question: The line C represented by which of the following equation does not intersect with the line represented by y = 3x^2+5x+1
(A) y = 2x^2+5x+1
(B) y = x^2+5x+2
(C) y = 3x^2+5x+2
(D) y = 3x^2+7x+2
(E) y = x^2+7x+1
Rationale: concept of slope for linesparabolas are different. Bunuel, please correct if I am wrong. Also please help to solve this problem if its a GMAT type question.
The general form of parabolic equ. is y^2= 4ax which implies the axis is x or x^2 = 4ay where axis is y.
We have a similar form as x^2 = 4ay.
here the vertex is origin.
So if we have same values of x and y but constant term changes then we will have parallel parabolas.
This is same as for straight line C which are parallel for different values of constant term c
ax + by +c1 = 0 and ax +by+ c2 =0
We have quadratic equations. These equations when drawn give parabolas, not lines. The question is: which of the following parabolas does not intersect with the parabola represented by y=3x^2+5x+1.C
Answer: (C) y = 3x^2+5x+2
Question: On July 1 of last year, total employees at company E was decreased by 10 percent. Without any change in the salaries of the remaining employees, the average (arithmetic mean) employee salary was 10 percent more after the decrease in the number of employees than before the decrease. The total of the combined salaries of all the employees at Company E after July 1 last year was what percent W of thatbeforeJuly 1 last year?
(A) 90%
(B) 99%
(C) 100%
(D) 101%
(E) 110%
Rationale: the total number of employees = n
the average salary = x
total salary to all emplyoees = xn
after
the total number of employees = n - 0.1n = 0.9n
the average salary = x + 10% of x = 1.1x
total salary to all emplyoees = 0.9n (1.1x)
total salary after as a % of total salary before W= [0.9n (1.1x)]/xn= 0.99 or 99%=B
Answer: (B) 99%
Question: If X = 2 + 1/(1+1/(1-1/2))then the value of 6x+7/3?
(A) 9 2/3
(B) 16 1/3
(C) 11
(D) 11 2/3
(E) 12
Rationale: X = 2 + 1/(1+1/(1-1/2))
= 2 + 1/(1+2)
= 2 + 1/3
X = 7/3 ==> 6X + 7/3 => 6(7/3) + 7/3
==> 42/3 + 7/3
==> 49/3
==> 16 1/3.
B)
Answer: (B) 16 1/3
Question: A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 15 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?
(A) 20
(B) 105
(C) 59
(D) 90
(E) 100
Rationale: to choose the sample of 2 customers from 15. it can be done 15C2 possible ways.
So the answer is B 105
Answer: (B) 105
Question: A photo-mat shop charges $0.55 for the first photo inside a film, and 30% cents less for each additional photo. How many photos can we develop with $52.58 if each film contains 32 photos?
(A) 4 films and 12 photos
(B) 5 films and 6 photos
(C) 5 films and 14 photos
(D) 6 films and 4 photos
(E) 6 films and 28 photos
Rationale: 1st photo = 0.55
Subsequent = 0.55*0.6=0.33
Price of 1 full film=0.55+0.33*35=12.1
Price of 4 full film = 12.1*4=48.4
52.58-48.4=4.18
4.18=0.55+0.33x
x=11
52.58--->5 full films and 1+11=14 photos
Answer: C
Answer: (C) 5 films and 14 photos
Question: A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone?
(A) 30 days
(B) 40 days
(C) 50 days
(D) 60 days
(E) 70 days
Rationale: Let A's 1 day's work = x and B's 1 day's work = y.
Then, x + y =1/30 and 16x + 44y = 1.
Solving these two equations, we get: x =1/60	and y =1/60
B's 1 day's work =	1/60	.
Hence, D alone shall finish the whole work in 60 days.
Answer : D
Answer: (D) 60 days