mathewhe/aqua_rat huggingface dataset:
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
(A) 42 6/9%
(B) 42 8/7%
(C) 49 6/7%
(D) 42 6/7%
(E) 32 6/7%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer:D
Answer: (D) 42 6/7%
Question: There are two numbers. If 10% of the first number is added to the second number, then the second number increases to its six-fifth. What is the ratio of the first number to the second number?
(A) 3 : 2
(B) 4 : 3
(C) 8 : 7
(D) 5 : 8
(E) 2 : 1
Rationale: Let the two numbers be x and y.
(1/10) * x + y = (6/5) * y
(1/10) * x = (1/5) * y
x/y = 2/1 = 2/1
The answer is E.
Answer: (E) 2 : 1
Question: There are 200 female managers in a certain company. Find the total number W of female employees in the company, if 2/5 of all the employees are managers and 2/5 of all male employees are managers.
(A) 300
(B) W=400
(C) W=500
(D) W=600
(E) None of these
Rationale: {Managers} = {Female Managers} + {Male Managers};
We are told that the total number of managers in the company is 2/5 of all the employees , thus{Managers} = 2/5 (M + F), where M and F are number of female and male employees, respectively.
Also, we know that 2/5 of all male employees are managers:{Male Managers} = 2/5 * Mas well as there are total of 200 female managers:{Female Managers} = 200;
Thus:2/5 (M + F) = 200 + 2/5 * M-->F = 500.
Answer: C.
Answer: (C) W=500
Question: X starts a business with Rs.56000. Y joins in the business after 4 months with Rs.44000. What will be the ratio in which they should share the profit at the end of the year?
(A) 21:11
(B) 11:21
(C) 22:23
(D) 25:23
(E) None of these
Rationale: Explanation :
Ratio in which they should share the profit
= Ratio of the investments multiplied by the time period
= 56000 * 12: 44000 * 8
= 56 * 12: 44 * 8
= 7*3: 11
= 21:11. Answer : Option A
Answer: (A) 21:11
Question: In a rectangular coordinate system, what is the area of a triangle whose vertices have the coordinates (-3, 0), (7, 4), and (7, -4)?
(A) 20
(B) 25
(C) 30
(D) 35
(E) 40
Rationale: The triangle is symmetric about the x-axis.
The part above the x-axis forms a triangle with a base of 10 and a height of 4.
The area of this part is (1/2)(10)(4).
We can double this to find the area of the whole triangle.
The total area is (2)(1/2)(10)(4) = 40.
The answer is E.
Answer: (E) 40
Question: The sum of two numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number.
(A) 72
(B) 64
(C) 84
(D) 12
(E) 92
Rationale: Let the numbers be x and (184-x). Then,
(x/3) - (184-x)/7 = 8
7x - 3(184-x) = 168
10x = 720, x = 72.
Hence the correct answer is option A) 72.
Answer: (A) 72
Question: A man sells an article at 15% loss. Had he sold it for Rs. 280/- more he could have gained 20%. What is the cost price of the article?
(A) Rs.420/-
(B) Rs.400/-
(C) Rs.460/-
(D) Rs.800/-
(E) None of these
Rationale: Explanation:
Short cut method:
Loss =====> 15 %
Profit ====> 20 %
~
----------------
35 % ---------> Rs. 280/-
100 % --------> Rs. 800/-
Answer: Option D
Answer: (D) Rs.800/-
Question: P software has coding line 5% more than N, N software has coding line 4/13 more than M. M software has 78 lines of coding. find P lines.
(A) 106
(B) 107
(C) 108
(D) 109
(E) 110
Rationale: M s/w has 78 line of code
N s/w has = 78+78*4/13= 102 line of code
P s/w 5% more N' code 102+5.1=107.1
or
107 line of code
ANSWER:B
Answer: (B) 107
Question: The bankers discount of a certain sum of money is Rs. 288 and the true discount on the same sum for the same time is Rs. 240. The sum due is:
(A) 1400
(B) 1420
(C) 1440
(D) 1460
(E) 1480
Rationale: Sum = (B.D*T.D)/(B.D-T.D)
(288*240)/288-240;
1440
ANSWER: C
Answer: (C) 1440
Question: Fifty five percent of a number is 21 less than four fifth of that number. What is the number ?
(A) 84
(B) 140
(C) 230
(D) 130
(E) 125
Rationale: Let the number be x.
Then, 4*x/5 â€“(55% of x) = 21
4x/5 â€“ 55x/100 = 21
x = 84.
Answer A.
Answer: (A) 84
Question: The only contents of a container are 4 blue disks and 8 green disks. If 3 disks are selected one after the other, and at random and without replacement from the container, what is the probability that 1 of the disks selected is blue, and 2 of the disks selected are green?
(A) 21/55
(B) 28/55
(C) 34/55
(D) 5/8
(E) 139/220
Rationale: Prob of selecting one blue and two green is (4*8*7/12*11*10)
one blue and two green can be arranged in 3!/2! ways
hence the prob becomes 3*4*8*7/12*11*10=28/55
Correct answer is B
Answer: (B) 28/55
Question: Which of the following is an integer?
I. 12! / 6!
II. 12! / 8!
III. 12! / 9!6!
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: 12!/6! = 12*11*10*9*8*7 which is an integer.
12!/8! = 12*11*10*9 which is an integer.
12!/9!6! = 12*11*10/ 6*5*4*3*2 = 11/6 which is not an integer.
The answer is D.
Answer: (D) I and II only
Question: a biker notices a certain number(2 digits number) on the milestone before starting the journey. After riding for an hour he notices a milestone with reversed digits of the previous number. Now after riding for another hour he notices that the number on a new milestone had same digits as the first one (in the same order) but with a "0" between the 2 digits. If the rider maintains a constant speed throughout, Calculate his speed.
(A) 40
(B) 45
(C) 50
(D) 55
(E) 60
Rationale: let first two digit number is xy = 10x + y
after one hour, the number is reversed yx = 10y + x
after another one hour, it x0y = 100x + y.
now xy < yx < x0y
so, (10y + x) - (10x + y) = (100x + y) - (10y + x)
or, 9(y - x) = 9(11x - y)
or, 12x = 2y
the above equation will be true only if x = 1 and y = 6.
hence, his speed is 45
ANSWER:B
Answer: (B) 45
Question: Foodmart customers regularly buy at least one of the following products: milk, chicken, or apples. 60% of shoppers buy milk, 50% buy chicken, and 25% buy apples. If 10% of the customers buy all 3 products, what percentage of Foodmart customers purchase exactly 2 of the products listed above?
(A) 5%
(B) 10%
(C) 15%
(D) 25%
(E) 30%
Rationale: The formula is
n(AUBUC) = n(A)+n(B)+n(C)-B+A-N
where B is both (it will sum of (AB), (BC), (CA)).
and A is All
and N is neither
so plugging in we get
100 = 60+50+25+10-B-0
B = 45.
exactly two = 45 - 3(10) = 15
subtracting 10% three times as this value is including in all the (AB), (BC), (CA).
Answer C
Answer: (C) 15%
Question: Abel can complete a work in 10 days, Ben in 12 days and Carla in 16 days. All of them began the work together, but Abel had to leave after 2 days and Ben 4 days before the completion of the work. How long did the work last?
(A) 6
(B) 7
(C) 7 2/3
(D) 9
(E) 10
Rationale: Abel in the 2 days that he worked completed 1/5 of the job = 4/5 remains
Then if Ben had to leave 4 days before the completion, this means that Carla had to work alone for these 4 days in which she completed 1/4 of the job.
Now together, Ben and Carla completed the job in (1/12 + 1/15)(t) = 11/20
3/20 (t) = 11/20 ---> t = 3 2/3
Therefore, these 3 2/3 days worked plus the 4 days that Carla had to work by herself add to 7 2/3 days
Answer: C
Answer: (C) 7 2/3
Question: plot ABCD is as shown in figure, where AF = 30 m, CE = 40 m, ED = 50 m, AE = 120 m. Find the area of the plot ABCD?
(A) 7207
(B) 7206
(C) 7203
(D) 7200
(E) 7201
Rationale: Area of plot ABCD = Area of ADE + Area of AFB + Area of BCEF
= 1/2 * 50 * 120 + 1/2 * 40 * 30 + 40 * 90 = 3000 + 600 + 3600
= 7200 sq.m
Answer: D
Answer: (D) 7200
Question: There are 1100 jelly beans divided between two jars, Jar X and Jar Y. If there are 500 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
(A) 550
(B) 600
(C) 650
(D) 700
(E) 750
Rationale: X+Y=1100 so Y=1100-X
X=3Y-500
X=3(1100-X)-500
4X=2800
X=700
The answer is D.
Answer: (D) 700
Question: M = {-6, -5, -4, -3, -2}
T = {-3, -2, -1, 0, 1, 2, 3, 4, 5}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?
(A) 0
(B) 3/7
(C) 2/5
(D) 1/2
(E) 5/9
Rationale: We will have a negative product only if 1, 2, 3, 4, or 5 are selected from set T.
P(negative product) = 5/9
The answer is E.
Answer: (E) 5/9
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.98 km
(B) 2.88 km
(C) 6.88 km
(D) 4.88 km
(E) 3.88 km
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: (B) 2.88 km
Question: Cindy's elephant balloon animal calls 3 long white balloons and 4 long black balloons. She needs to make 4 balloon animals for a child's party. If 12 long white balloons are used, then how many long black balloons are needed?
(A) 12
(B) 36
(C) 16
(D) 48
(E) 6
Rationale: Number of long white balloons needed per animal 3
Total number of animals needed 4
Total number of white balloons needed 3x4 = 12
Number of long black balloons needed per animal 4
Total number of animals needed 4
Total number of long black balloons needed 4x4 = 16
Answer 16
The correct answer is C
Answer: (C) 16
Question: If a point (x,y) is randomly selected within the square shown in the figure above, (the vertices are on 1,1 1,-1, -1,1 -1,-1) what are
the T odds that x^2+y^2>1?
(A) 1. pi/4
(B) 2. pi/16
(C) 3. T=1-pi/4
(D) 4. T=1-pi/16
(E) 5.4-pi
Rationale: area of the square will be 4, and the area of circle with center (0,0) and radius 1 will be pi.
then succesful outcomes = 4 - pi (the area where x2+y2 will be greater than 1)
total outcomes = 4
therefore probability = (4-pi)/4
C
Answer: (C) 3. T=1-pi/4
Question: In a competitive examination in state A, 6% candidates got selected from the total appeared candidates. State B had an equal number of candidates appeared and 7% candidates got selected with 80 more candidates got selected than A. What was the number of candidates appeared from each state?
(A) 6000
(B) 6500
(C) 7000
(D) 7200
(E) 8000
Rationale: Equal number of candidates appeared in each state.
In state A, 6% candidates got selected.
In state B, 7% candidates got selected.
Given that 80 more candidates got selected in state B than A.
Therefore, 1% of candidates appeared in each state
=
80
=80
=> 100% of candidates appeared in each state
=
80
×
100
=
8000
=80×100=8000
i.e., number of candidates appeared from each state = 8000
Option E
Answer: (E) 8000
Question: A can run 256 metre in 28 seconds and B in 32 seconds. By what distance A beat B?
(A) 32 metre
(B) 28 metre
(C) 23 metre
(D) 15 metre
(E) 28 metre
Rationale: Clearly, A beats B by 4 seconds
Now find out how much B will run in these 4 seconds
Speed of B = Distance/Time taken by B=256/32=8 m/s
Distance covered by B in 4 seconds = Speed Ã— time =8Ã—4=32 metre
i.e., A beat B by 32 metre
Answer is A
Answer: (A) 32 metre
Question: If 1/4 kg of tomato costs 60 paise, how many paise will 200 grams cost ?
(A) 45 paise
(B) 46 paise
(C) 47 paise
(D) 48 paise
(E) None of these
Rationale: Explanation :
1/4 kg means 250 gm
Less weight, less price (Direct Proportion)
So,
250:200::60:x
=>x=200*60/250
=>x=48
So 200 gm will cost 48 paise.
Answer : D
Answer: (D) 48 paise
Question: 6 mat-weavers can weave 6 mats in 6 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 14
Rationale: Let the required number of mats be x
More mat-weavers, more mats (direct proportion)
More days, more mats (direct proportion)
Hence we can write as
(mat-weavers)6:8
}::6:x
(days)6:8
⇒6×6×x=8×8×6
⇒x=10
ANSWER:B
Answer: (B) 10
Question: Mr X, a businessman, had income in the year 1995 such that he earned a profit of 20% on his investment in the business. In the year 1996 his investment was less by 6000 but still had the same income (Income = Investment + Profit) as that in 1995. Thus the per cent profit earned in 1996 increased by 6%. What was his investment in 1995?
(A) 100000
(B) 100500
(C) 126000
(D) Data inadequate
(E) None of these
Rationale: Let the investment of X in 1995 be x.
∴ Profit = x⁄5
∴ Income = (x + x⁄5) = 6⁄5x
Investment of company X in 1996 would be (x – 6000) From the question,
(x - 6000) × 126⁄100 = 6⁄5x ⇒ x = 126000
Answer C
Answer: (C) 126000
Question: The last day of a century cannot be :
(A) Monday
(B) Wednesday
(C) Friday
(D) Tuesday
(E) None of these
Rationale: 100 years contain 5 odd days. So, last day of 1st century is ‘Friday’
200 years contain (5 × 2) = 10 odd days = 3 odd days.
So, last day of 2nd century is ‘Wednesday’.
300 years contain (5 × 3) = 15 odd days = 1 odd day.
∴ Last day of 3rd century is ‘Monday’.
400 years contain 0 odd day.
∴ Last day of 4th century is ‘Sunday’
Since the order is continually kept in successive cycles,
we see that the last day of a century cannot be Tuesday,Thursday or Saturday.
Answer D
Answer: (D) Tuesday
Question: Two numbers are such that the square of one is 224 less than 8 times the square of the other. If the numbers be in the ratio of 3 : 4, the numbers are
(A) 6, 8
(B) 9, 12
(C) 12, 16
(D) 16, 20
(E) None
Rationale: Solution
Let the numbers be 3x and 4x. Then,
(4x)2 = 8 x (3x)2 - 224
‹=›16x2 = 72x2 - 224
‹=›56x2 = 224.
‹=›x2 = 4.
‹=›x = 2.
So, the numbers are 6 and 8.
Answer A
Answer: (A) 6, 8
Question: How many kg of sugar costing Rs.9/kg must be mixed with 27kg of sugar costing Rs.7/ kg so that there may be a gain of 10% the mixture at Rs.9.24/kg?
(A) 36
(B) 45
(C) 56
(D) 61
(E) 63
Rationale: Selling Price(SP) of 1 kg mixture= Rs. 9.24
Profit = 10%
Cost Price(CP) of 1 kg mixture =100(100+Profit%)×SP
=100(100+10)×9.24=100110×9.24=92.411= Rs.8.4
By rule of alligation,
CP of 1 kg sugar of 1st kind CP of 1 kg sugar of 2nd kind
Rs. 9 Rs. 7
Mean Price
Rs.8.4
8.4 - 7 = 1.4 9 - 8.4 = 0.6
i.e., to get a cost price of 8.4, the sugars of kind1 and kind2 should be mixed in the ratio 1.4 : 0.6 = 14 : 6 = 7 : 3
Suppose x
kg of kind1 sugar is mixed with 27 kg of kind2 sugar.
then x : 27 = 7 : 3
⇒3x=27×7⇒x=9×7=63
E
Answer: (E) 63
Question: A man walks from B to C, a distance of x miles, at 10 miles per hour and returns at 12 miles per hour. What is his average speed?
(A) 10.9 mph
(B) 9.6 mph
(C) 8.8 mph
(D) 8.4 mph
(E) 4 mph
Rationale: Total distance covered = 2x
Time taken12miles / hour = x/12 hrs
Time taken @ 10 miles / hour = x/10 hrs
Avg speed = 2x / (x/9 + x/12) = 10.9 mph
Ans is A
Answer: (A) 10.9 mph
Question: Today is Monday. After 61 days, it will be :
(A) Thursday
(B) Saturday
(C) Monday
(D) Sunday
(E) Wednesday
Rationale: Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.
Answer is B.
Answer: (B) Saturday
Question: If p and e are positive integers such that p > e > 1, what is the remainder when 92p × 5p+e + 11e × 6pe is divided by 10?
(A) A.0
(B) B.1
(C) C.3
(D) D.4
(E) E.5
Rationale: 92p × 5p+e + 11e × 6pe--1=B
Answer: (B) B.1
Question: The present ages of three persons in proportions 2 : 3 : 5. Five years ago, the sum of their ages was 35. Find their present ages (in years).
(A) 8, 20, 28
(B) 16, 28, 36
(C) 20, 35, 45
(D) 10,15,25
(E) None of these
Rationale: Explanation:
Let their present ages be 2x, 3x and 5x years respectively.
Then, (2x - 5) + (3x - 5) + (5x - 5) = 35
10x = 50
x =5
Their present ages are 2x = 10 years, 3x = 15 years and 5x = 25 years respectively.
Answer: D
Answer: (D) 10,15,25
Question: The speed of a boat in still water in 20 km/hr and the rate of current is 6 km/hr. The distance travelled downstream in 12 minutes is:
(A) 10.6
(B) 5.2
(C) 10.8
(D) 5.4
(E) 5.0
Rationale: Speed downstream = (20 + 6) = 26 kmph
Time = 24 minutes =12/60 hour = 1/5 hour
Distance travelled = Time × speed =1/5×26 = 5.20 km
Answer is B.
Answer: (B) 5.2
Question: In an entrance test, Deepika came across a mathematical patter problem.
If
6 / 7 = 2
3 / 9 = 7
8 / 2 = 6
Then
4 / 5 = ?
She was able to solve it in less than a minute. Can you?
(A) 0
(B) 4
(C) 6
(D) 12
(E) 15
Rationale: A
The answer is 0.
As
6 / 7 = 42 but the answer is written as 2
3 / 9 = 27 but the answer is written as 7
8 / 2 = 16 but the answer is written as 6
If we look at the answers, the second digit has been used in the problem.
Now, as
4 / 5 = 20 and the second digit is 0, the answer is 0.
Answer: (A) 0
Question: The output of a factory was increased by 10% to keep up with rising demand. To handle the holiday rush, this new output was increased by 10%. By approximately what percent would the output now have to be decreased in order to restore the original output?
(A) 20%
(B) 24%
(C) 30%
(D) 32%
(E) 17%
Rationale: The original output increases by 10% and then 10%.
Total % change = a + b + ab/100
Total % change = 10 + 10 + 10*10/100 = 21%
Now, you want to change it to 0, so,
0 = 21 + x + 21x/100
x = -21(100)/121 = 17% approximately
Answer is E
Answer: (E) 17%
Question: Mr Sharad started a business investing 50000. Four months later Mr Praveen joined the business by investing 90000. If the profit in the business at the end of the year was 22000 how much amount would Mr Praveen have received as the profit?
(A) 16000
(B) 14000
(C) 12000
(D) 11000
(E) None of these
Rationale: Ratio of their investment
= 50000 × 12 : 90000 × 8 = 5 : 6
\ Amount received by Praveen = 6⁄11 × 22,000
= 12,000
Answer C
Answer: (C) 12000
Question: Joe needs to paint all the airplane hangars at the airport, so he buys 360 gallons of paint to do the job. During the first week, he uses 1/3 of all the paint. During the second week, he uses 1/5 of the remaining paint. How many gallons of paint has Joe used?
(A) 168
(B) 144
(C) 175
(D) 216
(E) 250
Rationale: Total paint initially = 360 gallons
Paint used in the first week = (1/3)*360 = 120 gallons.
Remaning paint = 240 gallons
Paint used in the second week = (1/5)*240 = 48 gallons
Total paint used = 168 gallons.
Option A
Answer: (A) 168
Question: In an election only two candidates contested. A candidate secured 70% of the valid votes and won by a majority of 180 votes. Find the total number of valid votes?
(A) 450
(B) 570
(C) 480
(D) 520
(E) 550
Rationale: Let the total number of valid votes be x.
70% of x = 70/100 * x = 7x/10
Number of votes secured by the other candidate = x - 7x/100 = 3x/10
Given, 7x/10 - 3x/10 = 180 => 4x/10 = 180
=> 4x = 1800 => x = 450.
ANSWER:A
Answer: (A) 450
Question: A salesman travels a distance of 100 km in 5hours. How much faster in kilometer per hour, on an average, must he travel to make such trip in 1 hour less time?
(A) 2km/hr
(B) 3km/hr
(C) 5km/hr
(D) 7km/hr
(E) 10km/hr
Rationale: Time required = 5 hrs- 1hr = 4hr
Required speed = 100/4 = 25km/hr
Original speed = 100/5 = 20 km/hr
Difference = 25-20 = 5 km/hr
Answer is C
Answer: (C) 5km/hr
Question: At a dinner party, 5 people are to be seated around a circular table. 2 seating arrangements are considered different only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangements for the group?
A.
B.
C.
D.
E.
(A) 5
(B) 10
(C) 24
(D) 32
(E) 120
Rationale: let 1,2,3,4,5 are people.
1. we fix position of 1
2. we have 4*3=12 possible positions for left and right neighbors of 1.
3. for each position of x1y we have 2 possible positions for last two people: ax1yb and bx1ya.
Therefore, N=12*2=24 ANS:C
Answer: (C) 24
Question: In what time will a train 90 m long cross an electric pole, it its speed be 72 km/hr?
(A) 1.5
(B) 2.5
(C) 3.5
(D) 4.5
(E) 5.5
Rationale: Speed = 72 * 5/18 = 20 m/sec
Time taken = 90/20 = 4.5 sec.
Answer: D
Answer: (D) 4.5
Question: What do you get if you add 2 to 308 five times?
(A) 305
(B) 317
(C) 320
(D) 310
(E) 309
Rationale: D
310 , 310 , 310 , 310 , 310
Answer: (D) 310
Question: If 10 men can reap 120 acres of land in 15 days, how many acres of land can 20 men reap in 30 days?
(A) 120
(B) 240
(C) 360
(D) 1200
(E) 480
Rationale: 10 men 120 acres 15 days
20 men ? 30 days
120 * 20/10 * 30/15
120 *2 * 2
120 * 4 = 480
Answer:E
Answer: (E) 480
Question: A WNBA player just signed a new contract in which she will earn a 5% increase in base pay from last year to this year. Last year, she did not have a performance bonus; but this year, she will have the opportunity to earn up to a $40,000 performance bonus. If she earns the full performance bonus, her new effective salary will be a 7% raise over last year. What will her new salary be if she earns the full performance bonus?
(A) 2,120,000
(B) 2,140,000
(C) 2,180,000
(D) 2,240,000
(E) 2,260,000
Rationale: let x = last year's salary
the new base pay + 40,000 = the new effective pay
(1+.05)*x + 40,000 = (1+.07)*x
1.05x + 40,000 = 1.07x
40,000 = .02x
2,000,000 = x
thus the new salary = (1+.07)*2,000,000 = 2,140,000
B
Answer: (B) 2,140,000
Question: A marble shop contains 5 blue marbles, 5 red marbles, and 5 green marbles. If 2 marbles are purchased at random from the shop, what is the probability that the 2 marbles will be of the red?
(A) 5/15
(B) 2/21
(C) 20/15
(D) 5/210
(E) 4/14
Rationale: Of the 15 marbles we are wanting red:
Probability of choosing 1st red marble: 5/15
Probability of Choosing 2nd red marble: 4/14
Multiply and you get 20/210 simplified to 2/21
Answer B.
Answer: (B) 2/21
Question: How many three digits no. can be formed also including the condition that the no. can have at least two same digits ?
(A) 223
(B) 252
(C) 077
(D) 160
(E) 111
Rationale: Explanation:
Total number of 3 digit numbers = 9×10×10 = 900
Total number of numbers in which no digit repeats = 9×9×8 = 648
So the total number of numbers in which at least one digit repeats = 900 - 648 = 252
Answer:B
Answer: (B) 252
Question: Luke and Ben are in a relay race. Luke runs the first leg of the course in 59 seconds. Ben runs the second leg of the course in 48 seconds. What was the average time they took to run a leg of the course?
(A) 107 seconds
(B) 59 seconds
(C) 48 seconds
(D) 53.5 seconds
(E) 35.5 seconds
Rationale: (59 seconds +48 seconds)/2= 53.5 seconds
Correct option is: D
Answer: (D) 53.5 seconds
Question: A sports equipment store sold ping pong rackets for a total of $539. If the average (arithmetic mean) price of a pair of rackets is $9.8, how many pairs were sold?
(A) 55
(B) 100
(C) 490
(D) 500
(E) 980
Rationale: Average price for a pair of rackets = $9.8
Total cost = $9.8*x = $539
x = 55 pairs were sold.
ANSWER:A
Answer: (A) 55
Question: 0.032 x 0.0162 is equal to:
(A) 6.48 x 10(power -4)
(B) 6.84 x 10(power -4)
(C) 4.68 x 10(power -4)
(D) 5.184 x 10(power -4)
(E) None of them
Rationale: 32 x 162 = 5184. Sum of decimal places = 7.
So, 0.32 x 0.0162 = 0.0005184 = 5.184 x 10(power -4)
Answer is D
Answer: (D) 5.184 x 10(power -4)
Question: 18% of 680 - ? = 68.7
(A) 44.1
(B) 32.4
(C) 66.5
(D) 75.2
(E) 53.7
Rationale: E
53.7
(18 *680)/100 - ? = 68.7
? = 122.4 - 68.7
? = 53.7
Answer: (E) 53.7
Question: In the floor of a particular kitchen owned by an abstract artist, each row of tiles to the right of the first row contains two fewer tiles than the row directly to its left. If there are nine rows in all and a total of 450 tiles in the floor, how many tiles does the leftmost row contain?
(A) 52
(B) 58
(C) 60
(D) 64
(E) 68
Rationale: This question can be solved in a variety of ways: with algebra, by TESTing THE ANSWERS and by using a great Number Property shortcut involving consecutive integers.
We're given a few facts to work with:
1) There are 9 rows of tiles.
2) When going from 'left to right', each row contains TWO FEWER tiles than the one next to it.
3) There are a total of 450 tiles
We're asked how many tiles the left-most most row holds (meaning the one with the MOST tiles).
To start, 450 is divisible by 9, so we can figure out the AVERAGE number of tiles per row. That is 450/9 = 50. Since we're dealing with a set of 9 consecutive integers that differ by 2 each, we know that the '5th row' will have 50 tiles (the average). Then we just have to 'add 2s' until we get to the first row...
50 +2 +2 +2 +2 = 58.
Final Answer:
B
Answer: (B) 58
Question: In an examination, a student scores 3 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 30 questions and secures 130 marks, the no of questions he attempts correctly is :
(A) A)35
(B) B)40
(C) C)90
(D) D)88
(E) E)37
Rationale: Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
3x – (30 – x) = 130
=> 4x = 160
=> x = 40
Answer:B
Answer: (B) B)40