RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: The number N is H,284, where H represents the ten's digit. If N is divisible by 6, what is the value of H?
A.1
B.2
C.3
D.5
Answer: A.1
Explanation: If the number is divisible by 6, then the sum of the digits must also be divisible by both 3 and 2. Only 1 yields such a number.
Answer: A
Question: How many keystrokes are needed to type numbers from 8 to 180?
A.360
B.180
C.325
D.425
Answer: D.425
Explanation: Explanatory Answer
While typing numbers from 8 to 180, there are 2 single digit numbers: 8 and 9.
Each of these numbers requires one keystroke.
That is 2 key strokes.
There are 90 two-digit numbers: from 10 to 99.
Each of these numbers requires 2 keystrokes.
Therefore, 180 keystrokes to type the 2-digit numbers.
There are 81 three-digit numbers: from 100 to 180.
Each of these numbers requires 3 keystrokes.
Therefore, 243 keystrokes to type the 3-digit numbers.
Totally, therefore, one requires 2 + 180 + 243 = 425 keystrokes.
Choice D is the correct answer.
Question: Peter purchased 30 kg of rice at the rate of $11.50 per kg and 20 kg of rice at the rate of 14.25 per kg. He mixed the two and sold the mixture. Approximately what price per kg should be sell the mixture to make 30% profit?
A.17.2
B.15.3
C.16.3
D.19.3
Answer: C.16.3
Explanation: C
16.30
C.P. of 50 kg rice = (30 * 11.50 + 20 * 14.25) = $630.
S.P. of 50 kg rice = 130% of $630 = 130/100 * 630 = $819.
S.P. per kg = 819/50 = $16.38 = 16.30.
Question: How long does a train 100 m long traveling at 54 kmph takes to cross a station of 250 m in length?
A.22 sec
B.20 sec
C.15 sec
D.23 sec
Answer: D.23 sec
Explanation: D = 100 + 245 = 345 m
S = 54* 5/18 = 15
T = 345 * 1/15 = 23 sec
ANSWER:D
Question: River A and River B have a combined length of 650 miles and River B is 250 miles shorter than river A. How many miles long in river B?
A.100
B.200
C.300
D.400
Answer: B.200
Explanation: Total length of River A and River B is 650 miles.
Let X be the length of River A.
River B is 250 miles shorter than River A.
x+x-250=650
2x=650+250
x=450
Length of River A=450 miles.
Length of River B=450-250
=200 miles
Answer is option B
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is
A.1/37
B.1/36
C.1/28
D.1/29
Answer: B.1/36
Explanation: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6
= 216 ways.
Hence the probability is 6/216
= 1/36
Answer: B
Question: Jackson has $313,193 dollars in his investment accounts. What is the least amount of money (in whole number of dollars) that he must remove from his account if he wants to split this money evenly among nine new investors?
A.$1
B.$2
C.$3
D.$4
Answer: B.$2
Explanation: In order to divide the sum in 9 parts, the amount must also be divisible by 9
Divisibility rule of 9: The sum of the digits must be divisible by 9
Sum of digits of 313,193 = 20 and 18 is divisible by 9.
Hence we need to subtract 2 to this number for it to be divisible by 9
Correct Option: B
Question: The angles of a triangle are in the ratio 2: 3 : 4. Find the measurement of the 3 angles of triangle.
A.75°
B.25°
C.40°
D.80°
Answer: D.80°
Explanation: If the ratio of the three angles is 2:3:4, then the measures of these angles can be written as 2x, 3x and 4x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
2x + 3x + 4x = 180
Solve for x
9x = 180
x = 20
The measures of the three angles are
2x =2 x 2=40°
3x = 3 × 20 = 60°
4x = 4 × 20 = 80°
D
Question: Two numbers are respectively 20% and 25% more than a third number. The percentage that is first of the second is?
A.86%
B.98%
C.96%
D.06%
Answer: C.96%
Explanation: I II III
120 125 100
125----------120
100-----------? => 96%
Answer:C
Question: The price of a new SUV is $50,000 and you have $10,000 cash to make a down-payment. You will be able to finance the remainder of the balance over 60 months. Regarding the principle only, what percent of the original price of the SUV will you pay monthly?
A. 1/2 %
B. 1 %
C. 1 1/3 %
D. 2 %
Answer: C. 1 1/3 %
Explanation: A certain percentage of questions in the Quant section of the GMAT are just 'math questions' - you'll use a formula, do some calculations and you'll have the answer. This is one of those types of questions. You still have to write everything down and stay organized, but the work involved is relatively straight-forward.
Original price = $50,000.
Down-payment is $10,000, which is 20% of $50,000. ($10,000/ $50,000 x 100).
80% of original price remains. (100% - 20%)
80% to be paid over 60 months.
What percent of original price will be paid monthly? (80% ÷ 60 = 1 1/3 %)
C
Question: Shipment ------No. of Defective Chips/shipment---Total Chips in shipment
S2 -------------- 5 ------------------------ ----------------------12000
S3 -------------- 6 ----------------------------------------------- 18000
S4 -------------- 4 ----------------------------------------------- 16000
A computer chip manufacturer expects the ratio of the number of defective chips to be total number of chips in all future shipments equal to the corresponding ratio for shipmemts S1,S2,S3 and S4 comined as shown in the table above. What is the expected number Q of defective chips in a shipment of 60000 chips?
A.14
B.20
C.22
D.24
Answer: B.20
Explanation: I agree with your solution = 20. But the question is:
There are different combination to get 60,000 chips. For example: 1*S3 + 2*S4 + 2*S2. In this way, we ship 60,000 chips with only 6 + 4*2 + 2*2 = 18 defective chips, better than the average of 20.
The question is to find the expected number Q of defective chips, i guess it assume the minimum #, therefore it might not be 20.
Question: The area of a rectangular plot is 20 times its breadth. If the difference between the length and the breadth is 10 metres, what is its breadth?
A.10 metres
B.5 metres
C.7.5 metres
D.Data inadequate
Answer: A.10 metres
Explanation: L × B = 20 × B
∴ L = 20 m
and L – B = 10
∴ B = 20 – 10 = 10 m
Answer A
Question: Q' = 3Q - 3, what is the value of (7')' ?
A. 6
B. 106
C. 206
D. 306
Answer: D. 306
Explanation: (7')'=(3*7-3)'=18'=18*18-18=306
Answer D
Question: In a park there are two ponds with both brown ducks and green ducks. In the smaller pond there are 45 ducks and in the larger pond there are 55 ducks. If 20% of the ducks in the smaller pond are green and 40% of the ducks in the larger pond are green, then what percentage of ducks are green?
A.25%
B.27%
C.29%
D.31%
Answer: D.31%
Explanation: Number of ducks in small pond = 45
green ducks in small pond = 20 % of 45 = 9 ducks
Number of ducks in large pond = 55
green ducks in large pond = 40 % of 55 = 22 ducks
Total number of ducks = 45 + 55 = 100
total number of green ducks = 9 + 22 = 31 ducks
percentage of green ducks = 31/100 * 100 = 31%
Answer: D
Question: People were sitting in a circle.7th one is direct opposite to 18th one..Then how many were there in that group?
A.21
B.22
C.23
D.24
Answer: B.22
Explanation: 7 th one is exactly opposite represents half of circle. with 7 and 18 total members are 12
for remaing half=12*2-2(7th and 18th(already taken))=22
ANSWER:B
Question: If 3^x = 2, then 3^(4x+3) =
A.429
B.454
C.432
D.438
Answer: C.432
Explanation: 3^x=2
3^4x=2^4
3^4x=16
3^(4x+3)
=3^4x*3^3
=16*27
=432
Answer: C
Question: A perfect square is defined as the square of an integer and a perfect cube is defined as the cube of an integer. How many positive integers n are there such that n is less than 20,000 and at the same time n is a perfect square and a perfect cube?
A.3
B.4
C.5
D.6
Answer: C.5
Explanation: If n is a perfect square and a perfect cube, then n = a^6 for some integer a.
The numbers are 1^6=1, 2^6=64, 3^6= 729, 4^6=4096, 5^6=15,625.
The answer is C.
Question: There are 35 students in a hostel. If the no. of students increases by 7, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
A.38
B.40
C.42
D.45
Answer: C.42
Explanation: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
Question: A certain fraction has the same ratio to 1/36, as 4/7 does to 5/9. What is this certain fraction?
A.1/35
B.1/42
C.1/49
D.1/56
Answer: A.1/35
Explanation: x / (1/36) = (4/7) / (5/9)
x = 4*9*1 / 36*7*5 = 1/35
The answer is A.
Question: 34, 45, 56, 67,78, _ ?
A.33
B.82
C.99
D.89
Answer: D.89
Explanation: ANSWER: D
Question: Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
A.Rs.689
B.Rs.179
C.Rs.189
D.Rs.187
Answer: C.Rs.189
Explanation: CP per kg of mixture = [24(150) + 36(125)]/(24 + 36)
= Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100]
= Rs.189.
Answer:C
Question: A committee of four students has to be formed. There are five candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
A.3
B.4
C.5
D.6
Answer: D.6
Explanation: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE.
D
Question: Superman flies at a heroic rate of 10 miles per second- wow! What is his speed in kilometers per hour? [1km = 0.6 miles]
A.1,000
B.12,000
C.60,000
D.30,000
Answer: C.60,000
Explanation: To calculate the equivalent of kilometres in a mile
10 miles = 10*(0.6)^-1 = 16.6667 kilometres
In 1 hour there are 60 minutes
In 1 minute there are 60 seconds
So in 1 hour there are 3600 seconds
Speed in kmph = 16.6667 * 3600 = 60000
Correct answer - C
Question: A train met with an accident 90km away from station A. It completed the remaining journey at 5/6th of the original speed and reached station B 1hr 12mins late. Had the accident taken place 60km further, it would have been only 1hr late. what was the original speed of the train?
A.60 km/hr
B.55 km/hr
C.65 km/hr
D.90 km/hr
Answer: D.90 km/hr
Explanation: let the original speed be 6x. A/q, traveling 90 km at 5/6th of original speed costs him 12 minutes etc
90/5x =90/6x +12/90 -> x =10 , 9x= 90.
Ans D
Question: What is the principal sum?
I. The sum amounts to Rs. 690 in 3 years at S.I.
II. The sum amounts to Rs. 750 in 5 years at S.I.
III. The rate of interest is 5% p.a.
A.I and III only
B.II and III only
C.I and II only
D.Any two of the three
Answer: D.Any two of the three
Explanation: Explanation:
Clearly, any of the three will give us the answer
Answer: D
Question: How many times in a day, are the hands of a clock in straight line but opposite in direction?
A.21
B.22
C.17
D.26
Answer: B.22
Explanation: B
22
The hands of a clock point in opposite directions (in the same straight line) 11 times in every 12 hours. (Because between 5 and 7 they point in opposite directions at 6 o'clcok only).
So, in a day, the hands point in the opposite directions 22 times.
Question: A committee is to be formed by randomly choosing 5 people from 7 candidates. If Alice and Bob are candidates, what is the probability that Alice will be selected but Bob will not?
A.3/7
B.4/7
C.5/21
D.6/21
Answer: C.5/21
Explanation: The total number of ways to form a committee is 7C5=21.
The number of committees which include Alice but not Bob is 5C4=5.
The probability that Alice is selected but Bob is not selected is 5/21.
The answer is C.
Question: What approximate value should come in place of the question mark (?) in the following equation?64.85 Ã— 12.25 â€“ 30.22 Ã— 8.95 = (52 + ?) Ã— 10
A.5.39435
B.3.39435
C.2.39435
D.0.39435
Answer: D.0.39435
Explanation: Solve using approximation
Answer D
Question: A can do a piece of work in 12 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
A.2
B.4
C.18
D.6
Answer: C.18
Explanation: Explanation:
8/12 + 6/x = 1
X = 18 days
Answer:C
Question: A GOLF BALL HAS DIAMETER EQUAL TO 4.1CM. ITS SURFACE HAS 150 DIMPLES EACH OF RADIUS 2MM (0.2 CM) .CALCULATE TOTAL SURFACE AREA WHICH IS EXPOSED TO SURROUNDINGS ASSUMING THAT THE DIMPLES ARE HEMISPHERCAL.
A.81.62cm2
B.71.62cm2
C.61.62cm2
D.51.62cm2
Answer: B.71.62cm2
Explanation: the total surface area of the golf ball without considering the dimples is 4*3.14*sqrt(4.1/2).
Due to 150 pits on the surface a there will be a reduction in surface area of ball which will be equal to opening area of the dimples which is 150*3.04*sqrt(0.2). again due to formation of the pits there will be an increase in surface area due to hemispherical concave surface of the pits which will be 150*2*3.14*sqrt(0.2) .So, the total surface area will be 4*3.4*sqrt(4.1)-150*3.14*sqrt(.2)+150*2*3.14*sqrt(.2)=71.62cm2
ANSWER:B
Question: A and B can do a work in 5 days and 10 days respectively. A starts the work and B joins him after 3 days. In how many days can they complete the remaining work?
A.4/3 days
B.2 days
C.8 days
D.3 days
Answer: A.4/3 days
Explanation: Work done by A in 3 days = 3/5
Remaining work = 2/5
Work done by both A and B in one day = 1/5 + 1/10 = 3/10
Remaining work = 2/5 * 10/3 = 4/3 days.
Answer: A
Question: Excluding stoppages, the speed of a train is 45 kmph and including stoppages it is 36 kmph. Of how many minutes does the train stop per hour?
A.18
B.77
C.12
D.99
Answer: C.12
Explanation: T = 9/45 * 60
= 12
Answer:C
Question: How many different combinations of clothes can rahul make if he have 2 pairs of pants, 4 shirts, and 3 jackets?
A.10
B.18
C.24
D.20
Answer: C.24
Explanation: number of ways rahul can make is 4*3*2=24
Answer:C
Question: If x and y are odd integers, which of the following must always be a non-integer?
A.xy
B.x/y
C.y/x
D.xy/2
Answer: D.xy/2
Explanation: A) xy: (1)(1) = 1 and 1 is an integer. ELIMINATE
B. x/y: 1/1 = 1 and 1 is an integer. ELIMINATE
C. y/x: 1/1 = 1 and 1 is an integer. ELIMINATE
D. xy/2
E. -xy: -(1)(1) = -1 and -1 is an integer. ELIMINATE
As X and Y are odd, multiplication of x and y would result in odd integer
(Odd Integer)/2 will always be non integer
ANSWER:D
Question: A work can be finished in 11 days by forty women. The same work can be finished in eleven days by four men. The ratio between the capacity of a man and a woman is
A.4:1
B.3:4
C.2:3
D.3:2
Answer: A.4:1
Explanation: Work done by 40 women in 1 day = 1/11
Work done by 1 woman in 1 day = 1/(40Ã—11)
Work done by 4 men in 1 day = 1/11
Work done by 1 man in 1 day = 1/(4Ã—11)
Ratio of the capacity of a man and woman =1/(4Ã—11) : 1/(40Ã—11) = 1/4 : 1/40
= 1/1:1/4 = 4:1
Answer is A.
Question: Find the sum lend at C.I. at 5 p.c per annum will amount to Rs.441 in 2 years?
A.200
B.400
C.378
D.883
Answer: B.400
Explanation: 441 = P(21/20)2
P = 400
Answer: B
Question: A crate of mangoes contains one bruised mango for every thirty mango in the crate. If three out of every four bruised mango are considerably unsalable and there are 12 unsaleable mangoes in the crate then how many mango are there in the crate?
A.180
B.280
C.380
D.480
Answer: D.480
Explanation: Let the total no of mangoes in the crate be x
Then the no of bruised mango = 1/30 x
Let the no of unsalable mangoes =3/4 (1/30 x)
1/40 x =12
x=480
ANSWER D
Question: The ratio of radius of a circle and the side of a square is 2 : 7. Find the ratio of their areas:
A.2 : 1
B.4 : 7
C.8 : 77
D.4 : 49
Answer: D.4 : 49
Explanation: radius/side = 2/7
â‡’ area of circle/area of square= 4/49
Answer: D
Question: How many members are there between 1 to 100 which are divisible by 9 and the sum of two digits is 9?
A.13
B.11
C.7
D.9
Answer: D.9
Explanation: 9,18,27,36,45,54,63,72,81,90,99
9 is not a two digit number
99 sum is 18;
ans=9
ANSWER:D
Question: A patient is given exactly 750 milliliters of a mixture of two medications daily. Medication A contains 40% pain killer and medication B contains 20% pain killer. If the patient receives exactly 215 milliliters of pain killer daily, how many milliliters of medication B are in the mixture?
A.150
B.225
C.325
D.425
Answer: D.425
Explanation: Let there be A milliliters of Medication A
and B milliliters of Medication B
A+B = 750 -- 1
Medication A contains 40% pain killer and medication B contains 20% pain killer.
(40/100)*A + (20/100)*B = 215
=> (2/5)*A + (1/5)*B = 215
Multiplying by 5 , we get
2A + B = 1075 -- 2
Equation 2- Equation 1 , we get
A = 325
B = 425
Answer D
Question: The volumes of two cubes are in the ratio 27: 125, what shall be the ratio of their surface areas?
A.6:25
B.3:5
C.9:25
D.16:25
Answer: C.9:25
Explanation: a13 : a23 = 27 : 125
a1 : a2 = 3 : 5
6 a12 : 6 a22
a12 : a22 = 9 : 25
ANSWER:C
Question: Fifteen participants are participating in a competition. In how many ways can the first three prizes be won?
A.920
B.680
C.2730
D.720
Answer: C.2730
Explanation: Out of 15 participants, the first three prizes can be won in,
15P3 = 15! / (15 - 3)!
= 15 x 14 x 13
= 2730 ways
ANSWER:C
Question: A man spend 1/5 of his salary on food , 1/10 of his salary on house rent and 3/5 salary on clothes. he still has $16000 left with him. find salary..
A.$10800
B.$18000
C.$160000
D.$1800
Answer: C.$160000
Explanation: [1/(x1 / y1 + x2/y2 + x3/y3)] * Total amount= Balance amount
[1-(1/5 + 1/10 + 3/5)} * total salary= $16000, = [1-9/10] * Total salary = $16000, Total salary = $16000*10 = $160000, correct answer (C)
Question: Katie has 9 employees that she must assign to 3 different projects. If 3 employees are assigned to each project and no one is assigned to multiple projects, how many different combinations S of project assignments are possible?
A.252
B.1,680
C.2,340
D.362,880
Answer: B.1,680
Explanation: The ways to select three employees out of 9 for first project = 9C3
The ways to select three employees out of Remaining 6 for Second project = 6C3
Third Project already has the group of three to be assigned to it so need to select that
So total ways to assign 3 employees to each of 3 projects S= 9C3 * 6C3 * 1 = 1,680
Answer: Option B
Question: A car travels the first 1/3 of certain distance with a speed of 10km/hr the next 1/3 distance with a speed of 20 km/hr, and the last 1/3 distance with a speed of 10 km/hr. the average speed of the car for the whole journey is?
A.12km/hr
B.18km/hr
C.89km/hr
D.52km/hr
Answer: A.12km/hr
Explanation: Let the whole distance travelled be x km
and the average speed of the car for he whole journey be y km/hr
then (x/3)/10+(x/3)/20+(x/3)/10=x/y
x/30+x/60+x/30=x/y
1/12y=1
y=12km/hr
Answer(A)
Question: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month. Of the geese that survived the first month, 3/5 did not survive the first year. If 125 geese survived the first year and if no more than one goose hatched from each egg, how many goose eggs were laid at the pond?
A. 280
B. 400
C. 540
D. 625
Answer: D. 625
Explanation: Of the goose eggs laid at a certain pond, 2/3 hatched and 3/4 of the geese that hatched from those eggs survived the first month:
2/3*3/4 = 1/2 survived the first month.
Of the geese that survived the first month, 3/5 did not survive the first year:
(1-3/5)*1/2 = 1/5 survived the first year.
120 geese survived the first year:
1/5*(total) = 125 --> (total) = 625.
Answer: D.
Question: Calculate the share of profit made by 2 business partners, who invested $800 and $1200 respectively in a business if the profit made is $600.
A.$241,$360
B.$240,$2260
C.$240,$360
D.$230,$360
Answer: C.$240,$360
Explanation: A:B = 800:1200
A:B = 2 : 3
A's share = 600*2/5 = $240
B's share = 600*3/5 = $360
Answer is C
Question: What is the average of xx, 2x2x, and 66?
A.x+2
B.x+3
C.x+2x+2
D.x+4
Answer: C.x+2x+2
Explanation: By the definition of an average, we get:
x+2x+63=3x+63x+2x+63=3x+63
=3(x+2)3=x+2.=3(x+2)3=x+2.
Hence, the answer is x+2x+2 or Option C
Question: If the average (arithmetic mean) of x, x + 2, and x + 4 is 73, what is the value of x?
A.71
B.75
C.85
D.83
Answer: A.71
Explanation: AM of x, x + 2, and x + 4 = x + (x + 2) + (x + 4) / 3 = 3x + 6 /3 = x + 2
Given that x + 2 = 73
x = 71
Answer : A
Question: The ratio of number of students studying Arts, Commerce and Science in a College is 3 : 5 :4. What is the new ratio of the number of students studying Arts, Commerce and Science respectively if there is an increase of 20%, 40% and 25% in the number of students studying Arts, Commerce and Science?
A.18 : 35 : 50
B.3 : 10 : 10
C.4 : 8 : 5
D.8 : 35 : 25
Answer: D.8 : 35 : 25
Explanation: Suppose the number of students studying Arts, Commerce and Science be 3x, 5x and 4x respectively.
When their numbers are increased by 20%, 40% and 25% respectively the new ratio becomes
3x × 120% : 5x × 140% :
4x × 125% = 36 : 70 : 50
= 18 : 35 : 25
Answer D
Question: Find the Missing Number 1, 5, 13, 25, ?
A.41
B.44
C.23
D.26
Answer: A.41
Explanation: 5-1=4
13-5=8
25-13=12
So,
41-25=16
ans- 41
ANSWER:A
Question: Lucy deposited $62500 in an investment fund that provided 22 percent annual return compounded quarterly. If she made no other transactions with the fund, in how much time, in years, did her investment earn a total interest of $5100?
A.1/2
B.1/7
C.3
D.6
Answer: B.1/7
Explanation: A = P + I = 62500 + 5100 = 67600
67600 = 62500(1 + 22/4*100)^(4t)
t = 1/7 yrs
Answer: B
Question: What is the greatest prime factor of 5^6 - 1?
A.29
B.31
C.37
D.41
Answer: B.31
Explanation: 5^6-1 = (5^3-1)(5^3+1) = 124*126 = 4*31*3*42
The answer is B.
Question: Which of the following inequalities has a solution set, when graphed on the number line, is a single line segment of finite length?
A.2 <= 8x+10 <= 6
B.2 <= 34x+4 <= 6
C.2 <= 3x+4 <= 6
D.2 <= 3465x+4 <= 6
Answer: C.2 <= 3x+4 <= 6
Explanation: The key words in the stem are:a singleline segment offinite length
Now, answer choices A, B, and C can not be correct answers as solutions sets for these exponential functions are not limited at all (>= for even powers and <= for odd power) and thus can not be finite (x can go to + or -infinity for A and C and x can got to -infinity for B). As for D: we have thatabsolute valueof x is between two positive values, thus the solution set for x (because of absolute value) will be two line segments which will be mirror images of each other.
Answer: C.
Question: In a series of eight football matches between Germany and Argentina , the probability of Germany winning a match is 1/3 and the probability that the match ends in a draw is 1/4. If a win gets the team 2 points, a draw 1 point and a loss 0 Points, What is the probability that Germany will end up in 8 draws in the series?
A.24/576
B.125/864
C.1/25
D.1/65536
Answer: D.1/65536
Explanation: Since the probability of a draw is 1/4, then the probability of 8 draws in 8 matches is (1/4)^8=1/65536.
Answer: D.
Question: The perimeter of a rectangle is equal to the perimeter of aright-angled triangle of height 12 cm. If the base of the triangle is equal to the breadth of the rectangle, what is the length of the rectangle”
A.18 cm
B.24 cm
C.22 cm
D.Data inadequate
Answer: D.Data inadequate
Explanation: P = 2(l + b) = L + B + h = L + b + 12.
Data inadequate.
Answer D
Question: At a meeting, 25 attendants used a pencil and 15 attendants used a pen. If exactly 20 attendants used only one of the two types of writing tools, how many attendants wrote with both types of writing tools?
A.10
B.6
C.7
D.4
Answer: A.10
Explanation: Say x attendants wrote with both writing tools.
(25 - x) + (15 - x) = 20 --> x = 10.
Answer: A.