divelab/Sys2Bench huggingface dataset:
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)10 kmph
B)76 kmph
C)12 kmph
D)97 kmph
E)15 kmph
Rationale: Speed of the boat in still water
= (60+80)/2
= 70 kmph. Speed of the stream
= (80-60)/2
= 10 kmph.
Answer:A
Answer: A
Question: In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid vote polled in favour of candidate?
Options:
A)358000
B)368000
C)357000
D)358000
E)367000
Rationale: Total number of invalid votes = 15 % of 560000
= 15/100 × 560000
= 8400000/100
= 84000
Total number of valid votes 560000 – 84000 = 476000
Percentage of votes polled in favour of candidate A = 75 %
Therefore, the number of valid votes polled in favour of candidate A = 75 % of 476000
= 75/100 × 476000
= 35700000/100
= 357000
Answer:C
Answer: C
Question: The product of two numbers a and b equals one-quarter their average. What is a in terms of b?
Options:
A)a= b/(8b-1)
B)a= b/(7b-1)
C)a= b/(8b)
D)a= b/(8b-4)
E)a= 2b/(8b-1)
Rationale: a*b = ( a+b)/8
8ab =a+b
a= b/(8b-1)
ANSWER:A
Answer: A
Question: How many different positive integers are factors of 40?
Options:
A)3
B)2
C)1
D)6
E)4
Rationale: 2*20
4*10
8*5
Answer : D
Answer: D
Question: Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 91, the three numbers in order are?
Options:
A)39, 78, and 156
B)39, 156, and 78
C)78, 39, and 156
D)78, 156, and 39
E)156, 39, and 78
Rationale: Let the numbers be 2x, x and 4x
(2x + x + 4x)/3 = 91
7x/3 = 91
x = 39
The numbers in order are 78, 39, and 156
The answer is C.
Answer: C
Question: If |x – 9/2| = 5/2, and if y is the median of a set of r consecutive integers, where r is odd, which of the following must be true?
I. xyr is odd
II. xy(r^2 + r) is even
III. x^2y^2r^2 is even
Options:
A)II only is true
B)III only is true
C)I and III
D)II and III
E)I, II, and III
Rationale: given:
r is Odd
y is the median of odd numbers, hence y is Odd
x = solving the modulus you get 7 and 2. Hence x is Even or Odd
Therefore: r = O, y = O and x = O or E
Statement I = x*y*r = y*r*x = O x O x O/E = O x O/E = Odd or even. So False
Statement II = xy(r^2 + r) = O/E x O (O + O) = O/E x O(E) = O/E x E = Always Even. So true
Statement III. x^2y^2r^2 is even. E/O x O x O = Odd or even. Hence False.
Answer = A.
Answer: A
Question: How many seconds will a train 200 meters long running at the rate of 36kmph take to pass a certain telegraph post?
Options:
A)10sec
B)20sec
C)25sec
D)30sec
E)35sec
Rationale: Distance = length of train = 200meters
Speed = 36kmph = 36*5/18 = 10m/s
Required time = 200/10 = 20sec
Answer is B
Answer: B
Question: A machine, working at a constant rate, manufactures 18 pens in 30 minutes. How many pens does it make in 1 hr 45 min?
Options:
A)63
B)65
C)62
D)60
E)45
Rationale: Change 1 hr 45 min to 105 min. For this, we need to set up a simple proportion of pens per time
18/30= S/105
The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. Instead, cancel before you multiply. For what we can see this post. We can cancel 18/30 as 6/10
6/10= S/105
we can cross-multiply.
10*S = 6*105 = 630
If we divide both sides by 10,
S = 63
The machine would be 63 pens in 1 hr 45 min.
Answer: A
Answer: A
Question: How many two digit numbers of distinct digits can be formed by using digits 1, 2, 3, 4, 5, 6 and 7 such that the numbers are divisible by 2?
Options:
A)15
B)16
C)17
D)18
E)19
Rationale: 18
All numbers divisible by two must be even, therefore the two digit number must end in 2, 4, or 6. There are three possibilities for each odd number first digit and two combinations for each even first number digit. 4x3 + 3x2 =18
Correct answer is D.
Answer: D
Question: how many 4x5x8 cubes could fit in a 10x16x84 box?
Options:
A)84
B)90
C)85
D)77
E)64
Rationale: The answer is A) 84. The 10x16x84 box has an area of 13,440. The 4x5x8 cubes have an area of 160. If you divide 13,440 by 160, you get 84.
Answer: A
Question: If C = x% of y and B = y% of x, then which of the following is true?
Options:
A)1) C is smaller than B.
B)2) C is greater than B
C)3) Relationship between C and B cannot be determined.
D)4) If x is smaller than y, then A is greater than B.
E)5) None of the above
Rationale: Basically C = B = xy/100
None of the options mentions this; hence E.
Answer: E
Question: If p and q are positive integers, how many integers are larger than pq and smaller than p(q + 6)?
Options:
A)3
B)P + 2
C)6p – 1
D)2p – 1
E)2p + 1
Rationale: The number of integers between x and y, where x>y is (x-y)-1. For example, the number of integers between 1 and 5 is (5-1)-1=3: 2, 3, and 4.
Thus, the number of integers between pq and p(q+6)=pq+6p is (pq+6p-pq)-1=6p-1.
Answer: C.
Answer: C
Question: If a and b are positive even integers, and the least common multiple of a and b is expressed as a*b/r, which of the following statements could be false?
Options:
A)n is a factor of both a and b
B)(a*b)/n < ab
C)ab is multiple of 2.
D)(a*b)/n is a multiple of 2.
E)r is a multiple of 4.
Rationale: If we divide bynand get a multiple ofaand of b, then r must be a common factor. Answer A must be true.
Ifaandbare even integers, dividing by a factor (also an integer) results in something smaller than the productab. Answer B must be true.
If eitheraorbis even, thenabmust be even. Answer C must be true.
If both are even, the smallest either number can be is 2. Thus, the smallest common factor must be 2. Answer D must be true.
Ifbis 6 andais 2,nwould be 6, which is not 4. E can be false.
Answer: E
Question: If a square and a rhombus stand on the same base, then the ratio of the areas of the square and the rhombus is?
Options:
A)1:1
B)1:2
C)1:9
D)1:6
E)1:4
Rationale: A square and a rhombus on the same base are equal in area
Answer: A
Answer: A
Question: Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 50 marks. How many sums did Sandy get correct?
Options:
A)20
B)22
C)24
D)26
E)28
Rationale: Let x be the correct sums and (30-x) be the incorrect sums.
3x - 2(30-x) = 50
5x = 110
x = 22
The answer is B.
Answer: B
Question: A bookshop had science and art books in the ratio of 2:5. By the end of the week, 20% of both type of books were sold and 2240 books were unsold. How many art books were there at the starting?
Options:
A)1000
B)1200
C)1450
D)1550
E)2000
Rationale: science books sold = 2x × 0.2 = 0.4x
science books unsold = 2x – 0.4x = 1.6x
art books sold = 5x × 0.2 = x
art books unsold = 5x – x = 4x
total books unsold = 1.6x + 4x = 5.6x
5.6x = 2240
x = 400
2x science = 800
and 5x art books = 2000
E
Answer: E
Question: The cash difference between the selling prices of an article at a profit of 4% and 6% is Rs. 3. The ratio of the two selling prices is:
Options:
A)51:52
B)52:53
C)51:53
D)52:55
E)52:59
Rationale: Let C.P. of the article be Rs. x.
Then, required ratio = 104% of x / 106% of x
= 104/106 = 52/53 = 52:53
Answer: Option B
Answer: B
Question: the sum of seven consecutive integers is 980. How many of them are
prime?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: The middle number is 140 and the seven numbers are 137, 138, 139, · · · , 143.
Now 138, 140, and 142 are even, 141 is divisible by 3, and 143 - by 11. The remaining
numbers 137 and 139 are prime (it is easy to check that they are not divisible by 2,3,5,7
and 11).
correct answer C
Answer: C
Question: If J and X are integers, and 10J + X is odd, which of the following must be true?
Options:
A)J is odd
B)J is even
C)X is odd
D)X is even
E)both J and X are odd
Rationale: 10J will be always even as 10 has 2 as one of its factors
if 10J+X is odd, then the only possible explanation is that X is odd
correct answer C
Answer: C
Question: A car takes 6 hours to cover a distance of 180 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)10Kmph
B)20Kmph
C)15Kmph
D)30Kmph
E)25Kmph
Rationale: Time = 6
Distance = 280
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 180/9 = 20 Kmph
B)
Answer: B
Question: Which of the following is equal to 0.024 × 106 ?
Options:
A)2400000
B)240000
C)24000
D)2400
E)None of these
Rationale: Explanation :
0.024 × 106 = 0.024 × 1000000 = 24000. Answer : Option C
Answer: C
Question: In how many ways letters of the word RSCUPESATE be arranged?
Options:
A)256899
B)286457
C)395446
D)354678
E)302400
Rationale: RESUPESATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: E
Question: The following statements were made on the same day:
• It was Monday yesterday.
• Today is Thursday.
• The day after tomorrow will be Friday.
• Tomorrow will be Saturday.
• The day before yesterday was Tuesday.
Given that the number of correct statements above uniquely determines the day of the week
the statements were made, what day of the week were the statements made?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Thursday
E)none of the previous choices
Rationale: If all statements are false, the day is either Monday, Saturday, or Sunday. If exactly one
statement is true, the day is either Tuesday, Wednesday, or Friday. If exactly two statements
are true, the day is Thursday. Only in the later case the number of correct statements uniquely
determines the day of the week.
correct answer D
Answer: D
Question: How many positive integers less than 253 are multiple of 4 but NOT multiples of 6?
Options:
A)20
B)41
C)42
D)53
E)64
Rationale: From here, it might be easier to go up in bounds of 60, so we know that 61-120 gives 10 more numbers. 121-180 and 181-240 as well. This brings us up to 240 with 40 numbers. A cursory glance at the answer choices should confirm that it must be 42, as all the other choices are very far away. The numbers 244 and 248 will come and complete the list that’s (naughty or nice) under 250. Answer choice B is correct here.
Answer: B
Question: Of the 65 cars on a car lot, 30 have air-conditioning, 45 have air bag, and 12 have both air-conditioning and air bag. How many of the cars on the lot have neither air-conditioning nor air bag?
Options:
A) 2
B) 8
C) 10
D) 15
E) 18
Rationale: Total -Neither = All Air Conditioning + All air bags - Both
or 65 - Neither = 30 + 45 -12 = 63.
=> Neither = 2, hence C.
Answer : C
Answer: C
Question: The average of first five multiples of 6 is
Options:
A)3
B)18
C)9
D)12
E)15
Rationale: Solution
Average	= 6(1+2+3+4+5) / 5
= 90 / 5.
= 18
Answer B
Answer: B
Question: Reduce
368/552
to the lowest terms
Options:
A)2/3
B)2/9
C)2/8
D)16/25
E)None of these
Rationale: Explanation:
We can do it easily by in two steps
Step1: We get the HCF of 368 and 552which is 184
Step2: Divide both by 184, we will get the answer 2/3
Answer: Option A
Answer: A
Question: A box contains 3 white balls, 4 black balls and 5 yellow balls. In how many ways can 4 balls be drawn from the box, if at least one yellow ball is to be included in the draw?
Options:
A)652
B)547
C)425
D)356
E)346
Rationale: We may have (1 yellow and 3 others) or (2 yellow and 2 others) or (3 yellow and 1 others) or (4 yellow).
Therefore, Required number of ways= (4C1*8C3)+ (4C2*8C2)+ (4C3*8C1)+ (4C4)
= 4* 8*7*6/ 3*2*1 + 4*3/2*1 * 8*7/2*1 + (4C1*8) +1
= 224+168+32+1
= 425.
ANSWER:C
Answer: C
Question: If Susan can paint a house in 4 hours, and Jeff can paint the same house in 6 hours, how long will it take for both of them to paint the house together?
Options:
A)2.4 hr
B)2.6 hr
C)3.0 hr
D)5.0 hr
E)5.2 hr
Rationale: If Susan can paint the house in 4 hours, then in 1 hour she can paint 1/4 of the house.
If Jeff can paint the house in 6 hours, then in 1 hour he can paint 1/6 of the house.
Let x = number of hours it would take them together to paint the house so,
1/4 + 1/6 = 1/x
x=12/5 or 2.4 hours
Answer: A
Answer: A
Question: 3850 * 99
Options:
A)382550
B)384560
C)385690
D)389650
E)381150
Rationale: Explanation:
3850 * (100 - 1)
= 385000 - 3850
= 381150
Option E
Answer: E
Question: The average temperature for Tuesday, Wednesday and Thursday was 32°C. The average temperature for Wednesday, Thursday and Friday was 34°C. If the temperature on Friday be 44°C, what was the Temperature on Tuesday?
Options:
A)39°C
B)44°C
C)38°C
D)42°C
E)None of these
Rationale: Explanation:
T + W + T = 32 × 3 = 96°C
W+ T+ F = 34 × 3 = 102°C
Also, temperature on Friday = 44°C
Temperature on Tuesday = 96 +44 - 102 = 38°C
Answer: Option C
Answer: C
Question: Find the value of (1/(2*3))+(1/(3*4))+(1/(4*5))+(1/(5*6))+…..+ ((1/(9*10)).
Options:
A)2
B)2/5
C)3
D)3/5
E)4/5
Rationale: Given expression=((1/2)-(1/3))+((1/3)-(1/4))+((1/4)-(1/5))+((1/5)-(1/6))+….+ ((1/9)-(1/10))
=((1/2)-(1/10))=4/10 = 2/5.
ANSWER B 2/5
Answer: B
Question: At Didymus Corporation, there are just two classes of employees: silver and gold. The average salary of gold employees is $66,000 higher than that of silver employees. If there are 120 silver employees and 160 gold employees, then the average salary for the company is how much higher than the average salary for the silver employees?
Options:
A)$24,000
B)$28,000
C)$32,000
D)$36,000
E)$38,000
Rationale: The answer should be -> E. $38,000
Answer: E
Question: A person was asked to subtract 25% of a number from the original but he subtracted 25 from the number. His answer was 25 more than correct one. What was the original number?
Options:
A)200
B)100
C)250
D)150
E)160
Rationale: 25 + 25 = 50
25% ------ 50
100% ----- ? => 200
ANSWER A
Answer: A
Question: The largest one digit number which is a perfect cube, is:
Options:
A)7
B)8
C)9
D)1
E)0
Rationale: Explanation:
2*2*2 = 8
Answer: B
Answer: B
Question: On Monday, Lou drives his vehicle with 24-inch tires, averaging x miles per hour. On Tuesday, Lou switches the tires on his vehicle to 32-inch tires yet drives to work at the same average speed as on Monday. What is the percent change from Monday to Tuesday in the average number of revolutions that Lou's tires make per second?
Options:
A)Decrease by 14.3%
B)Decrease by 25%
C)Increase by 14.3%
D)Increase by 12.5%
E)Cannot be determined with the given information.
Rationale: 96 the LCM
On Tuesday 96/32 =3
On Monday 96/24 = 4
Therefore, 3-4/4 = -1/4=-25% decrease
Answer is B
Answer: B
Question: How many integers between 1 and 10^16 are such that the sum of their digits is 2?
Options:
A)106
B)116
C)126
D)136
E)146
Rationale: The integers with a sum of 2 are:
2, 20, 200,...,2*10^15 and there are 16 integers in this list.
Also, these integers have a sum of 2:
11
101, 110
1001, 1010, 1100
etc...
The number of integers in this list is 1 + 2 + ... + 15
Thus, the total number of integers is 1 + 2 + ... + 15 + 16 = 16*17/2 = 136
The answer is D.
Answer: D
Question: The difference between the length and breadth of a rectangle is 23 m. If its perimeter is 206 m, then its area is:
Options:
A)1570
B)3670
C)3510
D)1520
E)2520
Rationale: We have: (l - b) = 23 and 2(l + b) = 206 or (l + b) = 103.
Solving the two equations, we get: l = 63 and b = 40.
Area = (l x b) = (63 x 40) m^2 = 2520 m^2.
ANSWER:E
Answer: E
Question: A coin is weighted so that the probability of heads on any flip is 0.8, while the probability of tails is 0.2. If the coin is flipped 5 times independently, which of the following represents the probability that tails will appear no more than twice?
Options:
A)(0.8)^5 + 5(0.8)^4(0.2) + 10(0.8)^3(0.2)^2
B)(0.8)^5 + 4(0.8)^4(0.2) + 6(0.8)^3(0.2)^2
C)(0.6)^5 + 3(0.6)^4(0.4) + 2(0.6)^3(0.4)^2
D)(0.8)^5 + 2(0.8)^4(0.2) + (0.8)^3(0.2)^2
E)(0.6)^5 + (0.6)^4(0.4) + (0.6)^3(0.4)^2
Rationale: Probability of Head, P(H) = 0.8
Probability of Tail, P(T) = 0.2
Tail will appear NO more than twice
i.e. favourable cases
2 Tails and 3 Heads, Probability = 5C2*(0.8)^3*(0.2)^2
1 Tail and 4 Heads, Probability = 5C1*(0.8)^4*(0.2)^2
0 Tail and 5 Heads, Probability = (0.8)^5
Required Probability = Sum of all Favourable cases = (0.8)^5 + 5(0.8)^4(0.2) + 10(0.8)^3(0.2)^2
Answer: option A
Answer: A
Question: What number is 64 more than two-fourth of itself?
Options:
A)128
B)225
C)288
D)324
E)336
Rationale: 2/4x+64= x
That means 64=2/4x
x= 64*2= 128
A is the answer
Answer: A
Question: When a merchant imported a certain item, she paid a 7 percent import tax on the portion of the total value of the item in excess of $1,000. If the amount of the import tax that the merchant paid was $109.20, what was the total value of the item?
Options:
A)$1,600
B)$1,850
C)$2,250
D)$2,440
E)$2,560
Rationale: Let x be the value of the item.
0.07*(x-1000) = 109.20
x = 2560
The answer is E.
Answer: E
Question: Find the area of a parallelogram with base 26 cm and height 14 cm?
Options:
A)287 cm2
B)887 cm2
C)364 cm2
D)368 cm2
E)668 cm2
Rationale: Area of a parallelogram = base * height
= 26 * 14
= 364 cm2
Answer: C
Answer: C
Question: If an ant moves a distance x,then turn left 120 degree and travel x distance again and turn right 120 dgree and travel, he is 9 inches from the starting point, what is the value of x?
Options:
A)9√9
B)9√3
C)9√6
D)7√3
E)9√4
Rationale: See the above diagram. (A bit confusing though!!)
The ant starts from A travelled to B, turned 120 degrees left and travelled to C. and turned 120 degrees right and travelled to D.
From the diagram, ∠ACB=600∠ACB=600. As BC and AB are equal, ∠BCA=∠BAC=600∠BCA=∠BAC=600.
So ΔABCΔABC is equilateral.
Also ∠BCD=600∠BCD=600.
As, ∠ACB=∠BCD∠ACB=∠BCD equal, CB divides AD into two equal parts. Aso DE = 9/2.
In the triangle CED, Sin600=3–√2=92xSin600=32=92x
So x=9√3
Answer:B
Answer: B
Question: The ratio of the volumes of two cubes is 1000 : 3375. What is the ratio of their total surface areas?
Options:
A)81 : 121
B)4 : 9
C)729 : 1331
D)27 : 121
E)None of these
Rationale: Ratio of the sides = Â³âˆš1000 : Â³âˆš3375 = 10 : 15
Ratio of surface areas = 10^2: 15^2 =100 : 225 = 4: 9
ANSWER:B
Answer: B
Question: The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car?
Options:
A)89 kmph
B)92 kmph
C)75 kmph
D)65 kmph
E)77 kmph
Rationale: C
75 kmph
S = (90 + 60)/2 = 75 kmph
Answer: C
Question: How many positive integers less than 200 are there such that they are multiples of 13 or multiples of 14?
Options:
A)25
B)26
C)27
D)28
E)29
Rationale: 200/13 = 15 (plus remainder) so there are 15 multiples of 13
200/14 = 14 (plus remainder) so there are 14 multiples of 14
We need to subtract 1 because 13*14 is a multiple of both so it was counted twice.
The total is 15+14-1 = 28
The answer is D.
Answer: D
Question: The contents of a certain box consist of 14 apples and 26 oranges. How many oranges must be removed from the box so that 70 percent of the pieces of fruit in the box will be apples?
Options:
A)3
B)6
C)14
D)17
E)20
Rationale: The objective here is that 70% of the fruit in the box should be apples.
Now, there are 14 apples at start and there is no talk of removing any apples, so number of apples should remain 14 and they should constitute 70% of total fruit, so total fruit = 14/0.7 = 20
So we should have 20-14 = 6 oranges.
Right now, there are 26 oranges, so to get to 6 oranges, we should remove 26 - 6 = 20 oranges.
Answer E
Answer: E
Question: How many different three-digit multiples of 5 can be composed of digits 2, 6, 4, and 5 if none of the digits is repeated?
Options:
A)3
B)6
C)10
D)12
E)18
Rationale: can you explain your method. i solved it differently
XYZ, where Z must be 5. therefore 1 variation of digit in Z.
Y can be any of the 3 possible choices.
X can be any of the 2 possible choices.
2+3+1= 6
B
Answer: B
Question: A student scored an average of 55 marks in 3 subjects: Physics, Chemistry and Mathematics. If the average marks in Physics and Mathematics is 90 and that in Physics and Chemistry is 70, what are the marks in Physics?
Options:
A)86
B)165
C)76
D)155
E)26
Rationale: Given M + P + C = 55 * 3 = 165 --- (1)
M + P = 90 * 2 = 180 --- (2)
P + C = 70 * 2 = 140 --- (3)
Where M, P and C are marks obtained by the student in Mathematics, Physics and Chemistry.
P = (2) + (3) - (1) = 180 + 140 - 165
= 155
Answer:D
Answer: D
Question: A rectangular floor is covered by a rug except for a strip 2 meters wide along each of the four edge. If the floor is 10 meters by 8 meters, what is the area of the rug in square meters?
Options:
A)24
B)26
C)28
D)30
E)32
Rationale: A strip of 2 meters is covering the inner rectangular rug for all 4 sides.
Length of inner rug = 10-(2*2)
breadth of inner rug= 8-(2*2)
Area of Rug= 6 * 4 = 24 sq. mt
Ânswer: A
Answer: A
Question: A certain tax rate is $.82 per $100.00. What is the rate, expressed as a percent?
Options:
A)82%
B)8.2%
C)0.82%
D)0.082%
E)0.0082%
Rationale: Here in question it is asking $.82 is what percent of $ 100.Suppose $ .82 is x% of 100 means
100* (x/100) = .82
Hence x = .82 %
So answer is C.
Answer: C
Question: A boat goes 100 km downstream in 10 hours, and 80 km upstream in 20 hours. The speed of the stream is?
Options:
A)4km/h
B)3km/h
C)2km/h
D)(1/2) km/h
E)E)None
Rationale: 100 --- 10 DS = 10
? ---- 1
80 ---- 20 US = 4
? ----- 1 S = (10 - 4)/2
= 3 kmph
ANSWER:B
Answer: B
Question: A certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 10% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow
Options:
A)a) 2
B)b) 4.5
C)c) 0.196
D)d) 5.5
E)e) 3
Rationale: If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).
Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.
Therefore 6k = 0.1 (11 + 4k)
=> k = 0.196
Therefore the plant grows by 1 feet every day.
Option (C)
Answer: C
Question: Jerry began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Jerry?
Options:
A)35
B)55
C)39
D)40
E)60
Rationale: Carla starts 30 minutes later and it takes 3 hr for carla to meet Jerry
So Jerry total time travelled = 3hr + 30 minutes
Jerry distance = 30 * (3 1/2) = 105
so carla need to travle 105 to meet Jerry in 3 hrs
speed of carla = 105/3 = 35 miles per hour
Answer is A
Answer: A
Question: How many paying stones, each measuring 3 m * 2 m are required to pave a rectangular court yard 60 m long and 14m board?
Options:
A)99
B)140
C)26
D)17
E)12
Rationale: 60 * 14= 3 * 2 * x => x
=140
Answer: B
Answer: B
Question: Salaries of Ravi and Sumit are in the ratio 2:3. If the salary of each is increased by Rs. 4000, the new ratio becomes 40:57. What is Sumit's salary?
Options:
A)38000
B)46800
C)36700
D)50000
E)60000
Rationale: Explanation:
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then,
(2x+4000) / (3x+4000) = 40 / 57
⇒ 57 × (2x + 4000) = 40 × (3x+4000)
⇒ 6x = 68,000
⇒ 3x = 34,000
Sumit's present salary = (3x + 4000) = Rs.(34000 + 4000) = Rs. 38,000
Answer: A
Answer: A
Question: In how many ways can 5 boys be allotted four different study tables such that none of the study tables are empty and all the 5 boys are accommodated?
Options:
A)290
B)280
C)260
D)240
E)300
Rationale: 4 boys can be selected from 5 boys in 5C4 ways = 5
4 boys can be arranged in 4 rooms in 4! ways
and since 1 boy has to share a room with one of the 4 boys, therefore total ways = 2! = 2
Hence total number of ways in which allocation can be done = 5C4 * 4! * 2! = 5*2*4! =240
D
Answer: D
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
Options:
A)200 sq cm
B)72 sq cm
C)162 sq cm
D)Cannot be determined
E)None of these
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
ANSWER:D
Answer: D