RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Four circular cardboard pieces, each of radius 7cm are placed in such a way that each piece touches two other pieces. The area of the space encosed by the four pieces is
A.12
B.28
C.42
D.72
Answer: C.42
Explanation: required area = 14*14 - (4 * 1/4 * 22/7 * 7 *7) sq cm
= 196 - 154
= 42 sq cm.
Answer: C
Question: A man takes 3 hours 45 minutes to row a boat 10 km downstream of a river and 2 hours 30 minutes to cover a distance of 3 km upstream. Find the speed of the current.
A.1 km/hr
B.1/2 km/hr
C.3/4 km/hr
D.4 km/hr
Answer: C.3/4 km/hr
Explanation: Explanation:
First of all, we know that
speed of current = 1/2(speed downstream - speed upstream) [important]
So we need to calculate speed downstream and speed upstream first.
Speed = Distance / Time [important]
Speed upstream =(10/3 3/4)km/hr
=8/3km/hr
Speed Downstream = (3/2 1/2)km/hr
=6/5km/hr
So speed of current = 1/2(8/3−6/5)
=3/4km/hr
Option C
Question: if At what time between 7 & 2 will the hands of a watch point in opposite directions?
A.50 4/11 min past 4
B.50 4/11 min past 1
C.50 4/81 min past 7
D.50 4/81 min past 2
Answer: A.50 4/11 min past 4
Explanation: At 4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30min. spaces apart.
Minute hand will have to gain 5 min. spaces.
55min spaces are gained in 60 min.
5 min. spaces are gained in (60/55 * 50) min. or 54 6/11 min.
Required time = 54 6/11 min. past 4.
Answer: Option 'A'
Question: A and B can do a piece of work in 7 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
A.33
B.878
C.30
D.88
Answer: C.30
Explanation: C = 1/5 – 1/6 = 1/30 => 30 days
Answer: C
Question: In a race of 1000 m, A can beat by 100 m, in a race of 800m, B can beat C by 100m. By how many meters will A beat C in a race of 600 m?
A.12 m
B.25 m
C.127.5 m
D.32m
Answer: C.127.5 m
Explanation: Explanation:
When A runs 1000 m, B runs 900 m and when B runs 800 m, C runs 700 m.
When B runs 900 m, distance that C runs = (900 * 700)/800 = 6300/8 = 787.5 m.
In a race of 1000 m, A beats C by (1000 - 787.5) = 212.5 m to C.
In a race of 600 m, the number of meters by which A beats C = (600 * 212.5)/1000 = 127.5 m.
ANSWER C
Question: An urn contains 5 black and 3 white balls. Two balls are drawn from the urn one after the other
without replacement. What is the probability that both drawn balls are black?
A.1/5
B.3/7
C.5/14
D.3/5
Answer: C.5/14
Explanation: Let E and F denote respectively the events that first and second ball drawn
are black. We have to find P(E n F) or P (EF).
Now P(E) = P (black ball in first draw) = 5/8
Also given that the first ball drawn is black, i.e., event E has occurred, now there are 4 black balls and Eight white balls left in the urn. Therefore, the probability that the second ball drawn is black, given that the ball in the first draw is black, is nothing but the conditional probability of F given that E has occurred.
That is P(F|E) = 4/7
By multiplication rule of probability, we have
P (E n F) = P(E) P(F|E)
= 5/8 × 4/7 = 5/14
C
Question: Set S consists of integers {4, 7, 10, 14, 15}. If integer n is included in the set, the average (arithmetic mean) of set S will increase by 50%. What is the value of integer n?
A.28
B.32
C.36
D.40
Answer: D.40
Explanation: The average of the numbers in set S is 10.
If we increase the mean by 50%, the new mean is 15.
Thus, on average, 5 numbers increase by 5.
Therefore n = 15+25 = 40
The answer is D.
Question: What is least possible value of |23 - 7y| is
A.0
B.1
C.2
D.5
Answer: A.0
Explanation: Since y can be ANY number, we can minimize the value of |23 - 7y| by setting 23 - y equal to zero
If 23 - 7y = 0, then 23 = 7y, which means y = 23/7
In other words, when y = 23/7, we find that |23 - 7y| = 0
Answer:A
Question: find the terms which do not contain 7 between 1000 and 9999
A.9000
B.8000
C.8500
D.8800
Answer: A.9000
Explanation: Total number of four digit numbers =9000 (i.e 1000 to 9999 )
We try to find the number of numbers not having digit 2 in them.
Now consider the units place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Tens place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Hundreds place it can be selected in 9 ways (i.e 0,1,2,3,4,5,6,8,9)
Thousands place can be selected in 8 ways (i.e 1,2,3,4,5,6,,8,9) here '0' cannot be taken
Total number of numbers not having digit 7 in it =9 x 9 x 9 x 8 =5832
Also,Total number of numbers having digit 7 in it = 9000-5832 =3168
ANSWER:A
Question: If the sum of six numbers is between 135 and 164, then the average (arithmetic mean) of the six numbers could be which of the following?
A.15.4.
B.20.5.
C.25.5.
D.31.25.
Answer: C.25.5.
Explanation: 135/6=22.5
164/6=27.33
Only C fits in between these two limits.
Answer: C
Question: What number fits best in the missing place?
_	4	5	3	5
9	5	7	10	3
A.3
B.8
C.4
D.5
Answer: C.4
Explanation: C
4
5 = Five (four letters) => 4
7 = Seven (five letters) => 5
10 = Ten (three letters) => 3
3 = Three (five letters) => 5
Therefore, 9 = Nine (four letters) => 4.
Therefore the missing number is 4.
Question: A man rows his boat 84 km downstream and 48 km upstream, taking 2 hours each time. Find the speed of the stream?
A.6 kmph
B.5 kmph
C.9 kmph
D.8 kmph
Answer: C.9 kmph
Explanation: Speed downstream = d/t = 84/(2) = 42 kmph
Speed upstream = d/t = 48/(2) = 24 kmph
The speed of the stream = (42 - 24)/2 = 9 kmph
Answer:C
Question: How many of the positive factors of 25 , 150 and how many common factors are there in numbers?
A.2
B.4
C.3
D.5
Answer: C.3
Explanation: factors of 25 - 1, 5, 25
factors of 150 - 1, 2, 3, 5, 6, 10, 15, 25, 30, 50, 75, 150
Comparing both, we have three common factors of 25 and 150- 1,5,25
Answer(C)
Question: When n is divided by 12, the remainder is 2. What is the remainder when 4n is divided by 5?
A.1
B.2
C.3
D.4
Answer: C.3
Explanation: Let n=2 (leaves a remainder of 2 when divided by 15)
4n = 4(2) =8, which leaves a remainder of 3 when divided by 5.
Answer C
Question: A watch which gains 5 seconds in 3 minutes was set right at 7 a.m. In the afternoon of the same day, when the watch indicated quarter past 4 o'clock, the true time is?
A.4pm
B.3pm
C.5pm
D.6pm
Answer: A.4pm
Explanation: Time from 7 am to 4.15 pm = 9 hrs 15 min = hrs
3 min. 5 sec. of this clock = 3 min. of the correct clock.
Now 3min.5sec. is hrs of this clock = 3 min.is hrs of the correct clock
hrs of clock = hrs of the correct clock.
= 9 hrs of the correct clock.
The correct time is 9 hrs after 7 am. i.e., 4 pm.
Answer: A
Question: The measure of the side of a square is quadrupled. If x represents the perimeter of the original square, what is the value of the new perimeter?
A.3x
B.4x
C.9x
D.12x
Answer: B.4x
Explanation: Original perimeter = x
Hence original side = x/4
New side = 4x/4
New perimeter = 4*4x/4 = 4x
Correct Option: B
Question: A train travels from Albany to Syracuse, a distance of 100 miles, at the average rate of 50 miles per hour. The train then travels back to Albany from Syracuse. The total travelling time of the train is 5 hours and 24 minutes. What was the average rate of speed of the train on the return trip to Albany?
A.31.25
B.30
C.32
D.34
Answer: A.31.25
Explanation: 50*T =100 THEREFORE T = 100/50 =2
ON RETURN SPEED * ( 5.4 -2) =100 THEREFORE T = 100/3.2 =31.25
A
Question: What is the present worth of Rs. 396 due in 2 years at 5% simple interest per annum?
A.128
B.277
C.120
D.360
Answer: D.360
Explanation: Let the present worth be Rs. x. Then,
S.I. = (396 - x)
(x * 5 * 2) / 100 = (396 - x)
10x = 39600 - 100x
110x = 39600 => x = 360.
Answer: D
Question: If x is less than y by 45% then y exceed x by:
A.33.33%
B.25%
C.81.81%
D.66.66%
Answer: C.81.81%
Explanation: Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 45/(100-45)*100
=81.81%
ANSWER:C
Question: Meg and Bob are among the 4 participants in a cycling race. If each participant finishes the race and no two participants finish at the same time, in how many different possible orders can the participants finish the race so that Meg finishes ahead of Bob?
A.12
B.30
C.60
D.90
Answer: A.12
Explanation: Total # of ways the race can be finished is 4!. In half of the cases Meg finishes ahead of Bob and in other half Bob finishes ahead of Meg. So, ways Meg to finish ahead of Bob is 4!/2=12.
Answer: A.
Question: If GAVE is coded as 4657 and BAT is coded as 229. How is GATE coded?
A.4697
B.4967
C.4976
D.7496
Answer: A.4697
Explanation: g-4 a-6 e-7 from the code gate
t - 9 from bat
ANSWER:A
Question: Last year the price per share of Stock N increased by x percent and the earnings per share of Stock N increased by y percent, where x is greater than y. By what percent did the ratio of price per share to earnings per share increase, in terms of x and y?
A.x/y%
B.(100+y) %
C.100*(x-y)%
D.100*(x-y)/(100+y) %
Answer: D.100*(x-y)/(100+y) %
Explanation: Let P = the old price per share; E = the old earning per share. Thus P/E is the price to earning ratio before the increases
After the increase the new price is: P*(1+x/100) and the new earning is: E*(1 +y/100)
The new P/E is: (1+x/100)P/(1+y/100)E
The Percent of P/E increase = (new P/E - P/E)/(P/E). Subsititute new P/E to the equation we have:
[(1+x/100)/(1+y/100)*P/E - P/E]/(P/E)*100%. Simplifly the expression and you should get the answer to be:
100*(x-y)/(100+y) %
Answer : D
Question: A trader mixes 26 kg of rice at Rs. 10 per kg with 30 kg of rice of other variety at Rs. 20 per kg and sells the mixture at Rs. 20 per kg. His profit percent is:
A.No profit, no loss
B.30.23%
C.8%
D.10%
Answer: B.30.23%
Explanation: C.P. of 56 kg rice = Rs. (26 x10 + 30 x20) = Rs. (260 + 600) = Rs. 860
S.P. of 56 kg rice = Rs. (56 x 20) = Rs. 1120
Gain =260/860x100% = 30.23%
Answer: Option B
Question: Aram’s car was fined when he gave Joe and Peter a ride, so they decided to help Aram pay the fine. Joe paid $3 more than 1/4 of the fine and Peter paid $3 less than 1/3 of the fine, leaving pay $4 less than 1/2 the fine to complete the payment. What fraction of the fine did Aram pay?
A.$13
B.$15
C.$20
D.$28
Answer: C.$20
Explanation: As given Aram' payment is [1][/2]*Fine -4
i.e Total Fine = 2 * (Sam's payment + 4)
Now, as everything looks integer, Fine should be able to divide by 4 and 3 . Because Joe's contribution has 1/4 of the fine and Peter's contribution has 1/3 of the fine
So, that leads me to following :
Options , Aram's pay , Total Fine (F) , F/4 , F/3
A) , 13 , 34 , No i.e 34/4 , No i.e 34/3
B) , 14 , 38 , No , No
C) , 20 , 48 , Yes Yes
,
No need to further go on as we have got F/4 and F/3 correct, just for confirmation we go further
D) , 28 , 64 , Yes , No
E) , 48 , 104 , Yes , No
Correct answer is C
Question: When positive integer x is divided by 11, the quotient is y and the remainder is 4. When 2x is divided by 6, the quotient is 3y and the remainder is 5. What is the value of 7y – x ?
A.2
B.1
C.0
D.-1
Answer: D.-1
Explanation: (1) x = 11y + 4
(2) 2x = 18y + 5
Let's subtract equation (1) from equation (2).
7y + 1 = x
7y - x = -1
The answer is D.
Question: Find the sum The difference between the compound and S.I. on a certain sum of money for 6 years at 10% per annum is Rs.80 of money?
A.1000
B.1200
C.4800
D.3600
Answer: C.4800
Explanation: P = 80(100/10)6 => P = 1500
Answer: C
Question: A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?
A.4.3
B.7.2
C.2.3
D.3.2
Answer: B.7.2
Explanation: Explanation:
Speed = {\color{Blue} \left ( \frac{600}{5\times 60} \right )m/ sec =2m/ sec=\left ( 2\times \frac{18}{5} \right )km/hr=7.2km/hr}
Answer: B
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
A.150 m
B.350 m
C.300 m
D.240 m
Answer: D.240 m
Explanation: Speed =(54 x5/18m/sec) = 15 m/sec.
Length of the train = (15 x 20)m =300 m.
Let the length of the platform be x metres.
Then,x + 300/36= 15
x + 300 = 540
x = 240 m
Answer: D
Question: Two trains, each 100 m long, moving in opposite directions, cross other in 6 sec. If one is moving twice as fast the other, then the speed of the faster train is?
A.26 km/hr
B.17 km/hr
C.90 km/hr
D.77 km/hr
Answer: C.90 km/hr
Explanation: Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/6 = 3x => x = 25/2.
So, speed of the faster train = 50/2 = 50/2 * 18/5
= 90 km/hr.
Answer:C
Question: The length of a rectangular floor is more than its breadth by 200%. If Rs.441 is required to paint the floor at the rate of Rs.3/sq m, what would be the length of the floor?
A.12
B.18
C.20
D.21
Answer: D.21
Explanation: Let the length and the breadth of the floor be l m and b m respectively.
l = b + 200% of b = l + 2b = 3b
Area of the floor = 441/3 = 147 sq m
l b = 147i.e., l * l/3 = 147
l^2 = 441 => l = 21.
D
Question: Find the odd man out. 1, 8, 27, 64, 125, 196, 216, 343
A.64
B.196
C.216
D.1
Answer: B.196
Explanation: Explanation :
The pattern is 1^3, 2^3, 3^3, 4^3, 5^3, 6^3, 7^3.
196 is not a perfect cube
Answer : Option B
Question: The average age of a committee of 8 members is 40 years. A member aged 55 years retired and his place was taken by another member aged 39 years . The average age of
present committee is;
A.39 years
B.38 years
C.36 years
D.35 years
Answer: B.38 years
Explanation: Total age of the committee = 40*8 = 320,
Total age when a member is retired
and a new one was joined = 320-55 +39, =304
Average age of present committee = 304/8 = 38.
ANSWER:B
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq m?
A.4082.42
B.4082.38
C.4082.78
D.4082.4
Answer: D.4082.4
Explanation: Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 * 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
Answer: Option D
Question: Father is 5 times faster than son. Father completes a work in 40 days before son. If both of them work together, when will the work get complete?
A.8 1/0
B.8 1/3
C.8 1/8
D.8 1/6
Answer: B.8 1/3
Explanation: As efficiency is inversely proportional to days, If Father : son's efficiency is 5 : 1, then Days taken by them should be 1 : 5. Assume, the days taken by them are k, 5k.
Given that father takes 40 days less. So 5k - k = 40 ⇒⇒ k = 10
Father takes 10 days to complete the work. Total work is 10 x 5 = 50 units.
If both of them work together, they complete 5 + 1 units a day. 6/day. To complete 50 units, they take 50/6 = 8 1/3 days.
Ans: B
Question: Solve x2 â€“ 7x = 0
A.0,7
B.1,7
C.2,7
D.3,7
Answer: A.0,7
Explanation: This quadratic factors easily: Copyright Â© Elizabeth Stapel 2002-2011 All Rights Reserved
x2 â€“ 7x = 0
x(x â€“ 7) = 0
x = 0 or x â€“ 7 = 0
x = 0 or x = 7
The solution is x = 0, 7
ANSWER A
Question: Pumps A, B, and C operate at their respective constant rates. Pumps A and B, operating simultaneously, can fill a certain tank in 2 hours; pumps A and C, operating simultaneously, can fill the tank in 3/2 hours; and pumps B and C, operating simultaneously, can fill the tank in 2 hours. How many hours does it take pumps A, B, and C, operating simultaneously, to fill the tank.
A.1/3
B.1/2
C.1/4
D.1
Answer: C.1/4
Explanation: A+B =2; A+C =3/2 ,B+C =2 ; ADD THEN 2*(A+B+C) = 4+3/2 = 11/2
A+B+C = 11/4 HRS
C
Question: Raffle tickets numbered consecutively from 1 through 250 are placed in a box. What is the probability that a ticket selected at random will have a number with a hundreds digit of 2 ?
A.2/5
B.1/5
C.33/83
D.99/250
Answer: B.1/5
Explanation: SOLUTION
The number of integers from 1 to 250, inclusive is 250, out of which 100 (from 200 to 299) will have a hundreds digit of 2. Thus the probability is 50/250=1/5.
Answer: B
Question: Income of a company doubles after every one year. If the initial income was Rs. 4 lakhs.What would be the income after 5 years?
A.6.78 crores
B.1.28 crores
C.2.98 crores
D.3.78 crores
Answer: B.1.28 crores
Explanation: Income after 1 year=Rs. (4x2)lakhs
Income after 2 years= Rs. (4x2x2)lakhs
=Rs.4x4=16 lakhs
Income after 5years=Rs. (4x2^5)=Rs. 128 lakhs
=Rs. 1.28 crores
ANSWER: B
Question: A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
A.49
B.87
C.27
D.66
Answer: A.49
Explanation: Explanation:
Area of the wet surface = [2(lb + bh + lh) - lb]
= 2(bh + lh) + lb
= [2 (4 x 1.25 + 6 x 1.25) + 6 x 4]
= 49
Answer: A) 49
Question: We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $530. How many green hats did we buy?
A.A)36
B.B)20
C.C)40
D.D)42
Answer: B.B)20
Explanation: Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=530.
6(85-G)+7G=530.
510-6G+7G=530.
G=530-510=20.
The answer is B.
Question: The greatest common factor of 16 and the positive integer n is 4, and the greatest common factor of n and 45 is 3. Which of the following could be the greatest common factor of n and 120?
A.5
B.8
C.12
D.24
Answer: C.12
Explanation: n includes the factors 2^2 (but not 2^3) and 3 (but not 3^2 or 5)
120 = 8*3*5
The GCF is 4*3 = 12.
The answer is C.
Question: In his pocket, a boy has 3 red marbles, 5 blue marbles, and 6 green marbles. How many will he have to take out of his pocket to ensure that he has taken out at least one of each color?
A.10
B.11
C.12
D.13
Answer: C.12
Explanation: The worst case scenario would be that he has taken 5 blue and 6 green, a total of 11 marbles, and still doesn't have 3 distinct colors. But the next draw, marble number 12, will surely be red as only the red marbles are left in his pocket.
The answer is C.
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by :
A.5
B.7
C.9
D.11
Answer: D.11
Explanation: Sol.
Let the ten’s digit be x and unit’s digit be y. Then, number = 10x + y
Number obtained by interchanging the digits = 10y + x.
∴ (10x+y) + (10y + x) = 11 (x + y), which is divisible by 11.
Answer D
Question: If the sum of five consecutive even positive integers is A, then the sum of the next five even consecutive integers in terms of A is:
A.A+5
B.A+10
C.A+25
D.A+50
Answer: D.A+50
Explanation: In Case of Consecutive Integers or Integers in Arithmetic Progression Mean = Median
I.e. Median = A/5 = Mean = Third Integer
First Integer = A/5 - 4
Second Integer = A/5 - 2
Third Integer = A/5
Fourth Integer = A/5 + 2
Fifth Integer = A/5 + 4
i.e.
Sixth Integer = A/5 + 6
Seventh Integer = A/5 + 8
Eighth Integer = A/5 + 10
Ninth Integer = A/5 + 12
Tenth Integer = A/5 + 14
Now Mean of next 5 Integers = Median = A/5 + 5
i.e. Sum of Next 5 integers = (A/5 + 10)*5 = A+50
Answer: option D
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is?
A.17/27
B.17/70
C.17/90
D.17/20
Answer: D.17/20
Explanation: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(EᴜP) = 10/20 + 8/20 - 1/20 = 17/20
Answer: D
Question: Abby and Bobby type at constant rates of 70 words per minute and 60 words per minute, respectively. Bobby begins typing before Abby and has typed 600 words when Abby begins typing at 1:30 pm. If they continue typing at their respective rates, at what time will Abby have typed exactly 200 more words than Bobby?
A.1:40 PM
B.2:50 PM
C.2:00 PM
D.2:10 PM
Answer: B.2:50 PM
Explanation: Say time needed for Abby to type 200 more words than Bobby is t. In that time she would type 70t words and Bobby would type 60t words.
Now, total words typed by Bobby would be 600+60t and we want that number to be 200 less than 70t: 600+60t=70t-200 --> t=80.
1:30 PM + 80 minutes = 2:50 PM.
Answer: B.
Question: A man swims downstream 72 km and upstream 45 km taking 3 hours each time; what is the speed of the current?
A.1.5
B.3.5
C.4.5
D.2.5
Answer: C.4.5
Explanation: 72 --- 3 DS = 24
? ---- 1
45 ---- 3 US = 15
? ---- 1 S = ?
S = (24 - 15)/2 = 4.5
Answer:C
Question: A trader sells 85 meters of cloth for Rs. 8925 at the profit of Rs. 25 per metre of cloth. What is the cost price of one metre of cloth?
A.80
B.28
C.90
D.26
Answer: A.80
Explanation: Explanation:
SP of 1m of cloth = 8925/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 105 - Rs. 25 = Rs. 80.
Answer: A
Question: If 1 > 1 - ab > 0, which of the following must be true?
I. a/b > 0
II. ab < 1
III. a/b < 2
A.I only
B.II only
C.III only
D.I and II only
Answer: D.I and II only
Explanation: MANHATTAN GMATOFFICIAL SOLUTION:
You can manipulate the original compound inequality as follows, making sure to perform each manipulation on every term:
1 > 1 - ab > 0
0 > -a b > -1 Subtract 1 from all three terms.
0 < ab < 1 Multiply all three terms by -1 and flip the inequality signs.
Therefore you know that 0 < ab < 1. This tells you that ab is positive, so a/b must be positive (a and b have the same sign). Therefore, I must be true. However, you do not know whether a/b < 1, so II is not necessarily true. But you do know that ab must be less than 1, so III must be true.
Therefore, the correct answer is (D).
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number will be a solution to the equation (x-2)(x+1)(2X+5) = 0?
A.1/12
B.1/6
C.1/4
D.1/3
Answer: A.1/12
Explanation: x = -1
Prob = 1/12
Answer -A
Question: If the average (arithmetic mean) of 5 positive temperatures is x degrees Fahrenheit, then the sum E of the 3 greatest of these temperatures, in degrees Fahrenheit, could be
A. 6x
B. 4x
C. 5x/3
D. 3x/2
Answer: B. 4x
Explanation: 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<E<5x --> only option B fits.
Answer: B.
Question: What will be the result of 12^4+ 3 +2^9 +3 - 8/2 ?
A.58
B.14
C.145
D.69
Answer: D.69
Explanation: The multiplication(e.g. 12^4) and division(e.g. 8/2) is done first and then the sum(e.g. 48+3) and
subtraction (e.g.4-4), and the answer is 69, option D.
Question: A pet store holds cats and dogs. If the difference between the number of cats and the number of dogs is 7. What could be the ratio of Cats to dogs in the pet store?
A.1:3
B.1:4
C.28:35
D.2:5
Answer: C.28:35
Explanation: Say theratioof cats to dogs is a/b. Then thenumberof cats would be ax and thenumberof dogs bx, for some positive integer x.
We are told that ax - bx = 7 --> x(a - b) =7. Since 7 is a prime number it could be broken into the product of two positive multiples only in one way: x(a - b) = 1*7.
The above implies that either x = 1 and a - b = 7 or x = 7 and (a - b) = 1.
Therefore the correct answer should have the difference between numerator and denominator equal to 1 or 7.
For the original question only option which fits is E, 4:5. Cats = 7*4 = 28 and dogs = 7*5 = 35.
Answer: C.
Question: The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 16 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
A.40.2
B.40.4
C.40.6
D.40.8
Answer: B.40.4
Explanation: Sum of 10 numbers = 402
Corrected sum of 10 numbers
= 402 – 13 + 31 – 16 = 404
Hence, new average = 404⁄10 = 40.4
Answer B
Question: When the positive integer A is divided by 9 and 5, the remainder is 3 and 4, respectively. When the positive integer B is divided by 9 and 5, the remainder is 3 and 4, respectively. Which of the following must be a factor of A-B?
A.32
B.36
C.40
D.45
Answer: D.45
Explanation: A = 9k+3 = 5j+4
B = 9m+3 = 5n+4
A-B = 9(k-m) = 5(j-n)
Thus A-B is a multiple of 9 and 5, so it is multiple of 45.
The answer is D.