mathewhe/aqua_rat huggingface dataset:
Question: jaya two digits age when appended with the two digits age of amitabh the four digits number formed is a perfect square.what is the the sum of the four digits no.?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Min no could be = 7 (1024)
let jaya has two digits number= 10
and amitabh has two digits number=24
after appending=1024 which is perfect square of 32
and sum of four digits number 1024=7
ANSWER:B
Answer: (B) 7
Question: The average of runs of a cricket player of 10 innings was 33. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
(A) 77
(B) 79
(C) 85
(D) 87
(E) 89
Rationale: Explanation:
Average = total runs / no.of innings = 33
So, total = Average x no.of innings = 33 x 10 = 330.
Now increase in avg = 4runs. So, new avg = 33+4 = 37runs
Total runs = new avg x new no. of innings = 37 x 11 = 407
Runs made in the 11th inning = 407 - 330 = 77 Answer: A
Answer: (A) 77
Question: The weights of three boys are in the ratio 4:5:6. If the sum of the weights of the heaviest and the lightest boy is 45 kg more than the weight of the third boy, what is the weight of the lightest boy?
(A) 27 kg.
(B) 36 kg.
(C) 82 kg.
(D) 98 kg.
(E) 83 kg.
Rationale: Let the weights of the three boys be 4k, 5k and 6k respectively.
4k + 6k = 5k + 45
=> 5k = 45 => k = 9
Therefore the weight of the lightest boy = 4k = 4 * 9 = 36 kg.
Answer:B
Answer: (B) 36 kg.
Question: If (A+B) = 16, (B+C) = 9 and (C+D) = 3, what is the value of (A+D)?
(A) 10.
(B) 8.
(C) 7.
(D) 2.
(E) -2.
Rationale: Given A+B = 16 => A = 16 - B --> Eq 1
B+C = 9
C+D = 3 => D = 3 - C --> Eq 2
Then Eqs 1 + 2 => A + D = 16 - B + 3 - C
=> 19 - (B+C)
=> 19 - 9 = 10.
Option A...
Answer: (A) 10.
Question: A circle graph shows how the MegaTech corporation allocates its Research and Development budget: 14% microphotonics; 24% home electronics; 20% food additives; 29% genetically modified microorganisms; 8% industrial lubricants; and the remainder for basic astrophysics. If the arc of each sector of the graph is proportional to the percentage of the budget it represents, how many degrees of the circle are used to represent basic astrophysics research?
(A) 8°
(B) 10°
(C) 18°
(D) 36°
(E) 52°
Rationale: 14% microphotonics;
24% home electronics;
20% food additives;
29% genetically modified microorganisms;
8% industrial lubricants;
100-(14+24+20+29+8)=5% basic astrophysics.
5% of 360° is 18°.
Answer: C.
Answer: (C) 18°
Question: If the price of a TV is first decreased by 20% and then increased by 45%, then the net change in the price will be :
(A) 4% increase
(B) 10% increase
(C) 10% decrease
(D) 16% increase
(E) None of these
Rationale: Explanation :
Solution: let the original price be Rs. 100.
New final price = 145% of(80% of 100) =Rs. 145/100 * 80/100 * 100 = Rs. 116.
.'. Increase = 16%
Answer : D
Answer: (D) 16% increase
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
(A) 40%
(B) 44%
(C) 45%
(D) 48%
(E) 50%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120	x	m	= 6	x	m.
100	5
New breadth = 120	y	m	= 6	y	m.
100	5
New Area = 6	x x	6	y	m2	= 36	xy	m2.
5	5	25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11	xy x	1	x 100	%	= 44%.
25	xy
B
Answer: (B) 44%
Question: City A to city B, Andrew drove for 1hr at 50 mph and for 3 hours at 60 mph. What was the average speed for the whole trip?
(A) 57
(B) 57.5
(C) 61
(D) 61.5
(E) 62.5
Rationale: The total distance is 1×50+3×60=2301×50+3×60=230. And the total time is 4 hours. Hence,
Average Speed=(Total DistanceTotal Time)=2304=57.5
B
Answer: (B) 57.5
Question: The surface area of a sphere is 4πR2, where R is the radius of the sphere. If the area of the base of a hemisphere is 3, what is the surface area Q of that hemisphere?
(A)  6/π
(B)  9/π
(C)  6
(D)  9
(E)  12
Rationale: Given Area of the base of a hemisphere is 3 = PI * R^2
Thus R = Sqrt ( 3 / PI ) .
Surface area of whole sphere = 4*PI*R^2 .
= 4 * PI * 3 / PI
= 12 .
Since the hemisphere is half of a sphere the Surface area of the hemisphere = 12 / 2
= 6 ( curved part , not including the flat rounded base ) .
But the total surface area = 6 + Area of the base of a hemisphere .
= 6 + 3
= 9.
Answer is D !!
Answer: (D)  9
Question: On dividing 15 by a number, the quotient is 4 and the remainder is 3. Find the divisor?
(A) 3
(B) 6
(C) 9
(D) 12
(E) 15
Rationale: d = (D-R)/Q
= (15 - 3)/4
= 12/4 = 3
A)
Answer: (A) 3
Question: In how many different ways can 9 people be seated in a room with 11 chairs?
(A) 40,320
(B) 181,440
(C) 403,200
(D) 1,814,400
(E) 19,958,400
Rationale: Order doesn't matter
With 11 chairs and only 9 to seat
9!- Number of ways the 9 can seat on the chair
11C2 - Number of ways the 2 empty sits can be vary with the 9 seated
9! * 11C2 = 19,958,400 Answer - E
Answer: (E) 19,958,400
Question: The owner of a furniture shop charges his customer 24% more than the cost price. If a customer paid Rs. 8339 for a computer table, then what was the cost price of the computer table?
(A) 7297
(B) 2977
(C) 2871
(D) 6725
(E) 2981
Rationale: Explanation:
CP = SP * (100/(100 + profit%))
= 8339(100/124) = Rs. 6725.
Answer: D
Answer: (D) 6725
Question: As a bicycle salesperson, Norman earns a fixed salary of $20 per week plus $6 per bicycle for the first six bicycles he sells, $12 per bicycle for the next six bicycles he sells, and $18 per bicycle for every bicycle sold after the first 12. This week, Norman earned more than twice as much as he did last week. If he sold n bicycles last week and y bicycles this week, which of the following statements must be true?
I. y > 2n
II. y > n
III. y > 3
(A) I only
(B) II only
(C) I and II
(D) II and III
(E) I, II, and III
Rationale: This is kind of like doing your taxes, lets summarize the data in terms of bike sales and salary -
0 Bikes - $20
6 Bikes - $56
12 Bikes - $128
More than 12 bikes - 128 + 18*(n-12) where n is the total number of bikes sold (when n>12).
XN = cycles sold last week
NS = Salary last week.
Y = cycles sole this week
YS = Salary this week.
given YS>2NS
lets test all statements with N=0;
NS = 20
YS >40
True when Y = 4
satisfies all the statements but we can only be sure of iii as Y will only increase from here. So iii must be true. Eliminate A,B,C
lets test all statements with N=1;
NS = 26
YS>52
True when Y=6
Still satisfies all the statements - Nothing achieved
lets test all statements with N=6;
NS = 56
YS>112
True when Y = 11
This proves statement i wrong, hence eliminate E so we are left with
Answer D
Answer: (D) II and III
Question: x is the product of each integer from 1 to 100, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
(A) 5
(B) 6
(C) 8
(D) 10
(E) 12
Rationale: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*100 = 100!
No. of trailing zeros in 100! = 100/5 + 100/5^2 = 20+4 = 24
100^k = 10^2k → k = 24/2 = 12
E
Answer: (E) 12
Question: To mail a package, the rate is 30 cents for the first pound and 5 cents for each additional pound. Two packages weighing 4 pounds and 6 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
(A) Combined, with a saving of 20 cents
(B) Separately, with a saving of 5 cents
(C) Combined, with a saving of 25 cents
(D) Separately, with a saving of 15 cents
(E) Combined, with a saving of 22 cents
Rationale: 4 pounds cost = 30+3*5 = 45
6 pounds cost = 30+5*5 = 55
Total = 100
10 pounds cost = 30+ 9*5 =75 dif. 25
Answer : C
Answer: (C) Combined, with a saving of 25 cents
Question: A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different W arrangements of plays can be run, if the same play can’t be run more than once?
(A) 24
(B) 125
(C) 243
(D) 504
(E) 729
Rationale: Number of W ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
Answer: (D) 504
Question: On a game show, a contestant is given three keys, each of which opens exactly one of the three identical boxes.The contestant assigns each key to one of the boxes and wins the amount of money contained in any box that is opened by the key assigned to it. The first box contains $4, the second $400, and the third $4000. What is the probability that a contestant will win more than $4000?
(A) 2/6
(B) 1/6
(C) 1/8
(D) 1/3
(E) 1/2
Rationale: Let's call the boxes that contain $4, $400, and $4000, respectively, Box A, Box B, Box C. These are opened, respectively, by Key A, Key B, and Key C.
We want to know the probability of winning more than $4000. Notice that if the distribution of keys is:
Box A = Key B
Box B = Key A
Box C = Key C
then the contestant wins exactly $4000, not more than $4000. The only configuration that leads to winning more than $1000 is:
Box A = Key A
Box B = Key B
Box C = Key C
i.e., getting all three keys correct. That's the only way to be more than $4000. So, really, the question can be rephrased: what is the probability of guessing the order of keys so that each key matches the correct box?
Well, for a set of three items, the number of possible permutations is 3! = 3*2*1 = 6.
Of those 6 possible permutations, only one of them leads to all three keys being paired with the right box. So, the answer is
Probability = 1/6
Answer: B
Answer: (B) 1/6
Question: How many bricks, each measuring 5 cm x 11 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 2 cm?
(A) 5600
(B) 6000
(C) 2909
(D) 7200
(E) 8600
Rationale: Number of bricks =Volume of the wall/Volume of 1 brick =	(800 x 600 x 2)/(5 x 11 x 6) = 2909.
Answer: Option C
Answer: (C) 2909
Question: If x =- |x| , then which one of the following statements could be true?
I. x = 1
II. x < 0
III. x > 0
(A)  None
(B)  I only
(C)  II only
(D)  I and II
(E)  II and III
Rationale: Answer copied from NOVA guide
Statement I could be true because + 1 = −(+1) = −(1) = -1 .
Statement II could be true because the right side of the equation is always negative [ ± x = –(a positive number) = a negative number].
Now, if one side of an equation is always negative, then the other side must always be negative,
otherwise the opposite sides of the equation would not be equal.
Since Statement III is the opposite of Statement II, it must be false. But let’s show this explicitly:
Suppose x were positive. Then x = x, and the equation x = ± x becomes x = –x. Dividing both sides of this equation by x yields 1 = –1. This is contradiction.
Hence, x cannot be positive. The answer is (C).
Answer: (C)  II only
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
(A) 37.5
(B) 25.7
(C) 30.5
(D) 22.5
(E) 20.5
Rationale: 100 * 100 = 10000
110 * 125 = 13750
-----------
3750
10000 ------ 3750
100 ------- ? => 37.5%
ANSWER A
Answer: (A) 37.5
Question: In a new housing development, trees are to be planted along the sidewalk of a certain street. Each tree takes up one square foot of sidewalk space, and there are to be 10 feet between each tree. How many trees can be planted if the road is 166 feet long?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 16
Rationale: Let T be the number of trees. Then the length required for trees on the sidewalk will be 1*T= T
To maximize the number of trees, the number of 10 feet spaces between trees should be 1 less than total number of trees.
For example, If there are 3 trees, then there should be 2 spaces between them.
So the number of 10 feet spaces will be T-1. Then, the length of sidewalk required for 10 feet spaces will be 10*(T-1)
It is given that total lenght of sidewalk is 166 feet.
or 10(T-1)+T = 166
or 10T-10+T = 166
or T=16
Answer:- E
Answer: (E) 16
Question: The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: Explanation:
Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).
Answer D
Answer: (D) 19
Question: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the first is twice the previous term. What is the sum of the 16th, 17th terms in the sequence?
(A) 2^18
(B) 3(2^17)
(C) 7(2^16)
(D) 3(2^15)
(E) 7(2^15)
Rationale: the sequence comes out to be 2^0,2^1,2^2,2^3 and so on...
so 16th term will be 2^15
17th term 2^16
adding all three
we get
2^15+(2^15)*2
so answer is 2^15(1+2)=>3(2^15)
answer D
Answer: (D) 3(2^15)
Question: A train 110 m long is running with a speed of 84 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 6 sec
(C) 8 sec
(D) 4.4 sec
(E) 2 sec
Rationale: Speed of train relative to man = 84 + 6
= 90 km/hr.
= 90 * 5/18 = 25 m/sec.
Time taken to pass the men = 110/25
= 4.4 sec.
Answer:D
Answer: (D) 4.4 sec
Question: In Anthony's toy bin there are 17 red blocks. There are 8 more yellow blocks than red blocks. There are also 4 more blue blocks than red blocks. How many blocks are there in all?
(A) 22
(B) 11
(C) 29
(D) 63
(E) 34
Rationale: Step 1: Find the number of yellow blocks.
17 + 8 = 25
Step 2: Find the number of blue blocks.
17 + 4 = 21
Step 3: Find the total number of red, yellow, and blue blocks.
17 + 25 + 21 = 63
There are 63 blocks in Anthony's toy bin.
Answer is D.
Answer: (D) 63
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150m
(B) 288m
(C) 278m
(D) 229m
(E) 267m
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer: A
Answer: (A) 150m
Question: Four-ninths of a drink mix is dye and the rest is sugar. When the mix is added to water a gallon of drink is made that is 7.5% sugar. What percentage of the gallon is dye?
(A) 6
(B) 6.5
(C) 7.5
(D) 8
(E) 24
Rationale: The proportion of Dye and sugar will remain constant.
Dye/Sugar = (4/9)/(5/9) = x/7.5
=> 4/5 = x/7.5 => x = 4*7.5/5 = 6.
Answer is A.
Answer: (A) 6
Question: The three digits of a number add up to 14. The number is divisible by 5. The leftmost digit is double the middle digit. What is the product of the three digits?
(A) 40
(B) 72
(C) 78
(D) 90
(E) 125
Rationale: Say the three-digit number is abc.
The leftmost digit is double the middle digit --> a=2b;
The number is divisible by 5 --> c is either 0 or 5;
The three digits of a number add up to 13 --> a+b+c=14
So, either a+b+c=2b+b+0=14 or a+b+c=2b+b+5=14. The first equation does not give an integer value of b, so it's not the case. From the second we get that b=3 --> a=6 and c=5 --> a*b*c=90.
Answer: D.
Answer: (D) 90
Question: David deposited $5,000 to open a new savings account that earned six percent annual interest, compounded semi-annually. If there were no other transactions in the account, what the amount of money in David account one year after the account was opened?
(A)  $5,306
(B)  $6,120
(C)  $5,136
(D)  $5,405
(E)  $5,500
Rationale: Approach #1:
6 percent annual interest compounded semi-annually --> 3% in 6 moths.
For the first 6 moths interest was 3% of $5,000, so $150;
For the next 6 moths interest was 3% of $5,000,plus3% earned on previous interest of $150, so $150+$6=$156;
Total interest for one year was $150+$156=$306, hence balance after one year was $5,000+ $306=$5,306.
Answer: A.
Answer: (A)  $5,306
Question: A train moves with a speed of 162 kmph. Its speed in metres per second is
(A) 10.8
(B) 18
(C) 30
(D) 38.8
(E) 45
Rationale: Solution
Speed	= 108 Kmph
= (162 x 5/18)m/sec
= 45 m/sec.
Answer E
Answer: (E) 45
Question: If the average (arithmetic mean) of 102 consecutive odd integers is 414, then the least of these integers is
(A) a) 160
(B) b) 289
(C) c) 250
(D) d) 313
(E) e) 525
Rationale: A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.
There are 102 numbers in the set, and in a set with an even number of terms the median is just the average of the two most median terms (here the 51st and 52nd numbers in the set). This means that numbers 51 and 52 in this set are 413 and 415. Because we know that number 51 is 413, we know that the smallest number is 50 odd numbers below this, which means that it is 50*2 = 100 below this (every odd number is every other number). Therefore 413-100 = 313, answer choice D
Answer: (D) d) 313
Question: 40 is what percent of 160?
(A) 35%
(B) 40%
(C) 45%
(D) 50%
(E) 25%
Rationale: 40/160×100=25% ANSWER : E
Answer: (E) 25%
Question: Which of the following equations passes through the points (2,4) and (-3,-6)?
(A) y = (1/2)x - 2
(B) y = 2x
(C) y = (-1/2)x + 2
(D) y = 2x + 4
(E) y = 2x - 4
Rationale: Find slope first = (y1-y2)/(x1-x2) = (-6-4)/(-3-2) = 2
Using the point (2,4) in options
we get,
y = 2x as right answer.
Ans- B
Answer: (B) y = 2x
Question: Ratio between 2 numbers is 5 : 7 and their product is 560.what is the difference between 2 numbers?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 2
Rationale: Explanation:
x/y = 5/7
x × y = 560 ⇒ x = 560/y
Substituting this value in first equation, we get 560/yy=57560/yy=57 ⇒560y2=57560y2=57 ⇒ y = 28
x = 20
So difference between the numbers could be
x – y = –8
y – x = 8
Answer: C
Answer: (C) 8
Question: Three 8 faced dice are thrown together. The probability that all the three show the same number on them is ?
(A) 1/38
(B) 1/48
(C) 1/56
(D) 1/64
(E) 1/68
Rationale: It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555, 666, 777 and 888. Those are eight in number. Further the three dice can fall in 8 * 8 * 8 = 512 ways.
Hence the probability is 8/512 = 1/64
Answer:D
Answer: (D) 1/64
Question: The difference of two numbers is 1375. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?
(A) 240
(B) 272
(C) 295
(D) 360
(E) 252
Rationale: Let the smaller number be x. Then larger number = (x + 1375).
x + 1375 = 6x + 15
5x = 1360
x = 272
Smaller number = 270.
ANSWER B
Answer: (B) 272
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 7 : 5 and 1 : 2, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
(A) 1 : 1
(B) 2 : 3
(C) 5 : 2
(D) 10 : 11
(E) 7 : 9
Rationale: Mixture A has a total of 7 + 5= 12 parts. If in the final mixture this represents 6 parts, then the total number of parts in mixture B should be (12/6)*3 = 6.
So, we should take of mixture B a quantity with 3 and 6 parts, respectively.
This will give us in the final mixture (7 + 3) : (5 + 6), which means 10:11
Answer D.
Answer: (D) 10 : 11
Question: What is the sum of all the prime numbers greater than 10 but less than 40?
(A) 190
(B) 189
(C) 180
(D) 199
(E) 1981
Rationale: Required sum = (11 +13 + 17 + 19 + 23+ 29 + 31 + 37) = 180
Note: 1 is not a prime number
Answer C
Answer: (C) 180
Question: The fourth proportional to 5, 8, 15 is:
(A) 9
(B) 24
(C) 18
(D) 19
(E) 20
Rationale: Let the fourth proportional to 5, 8, 15 be x.
Then, 5 : 8 : 15 : x
5x = (8*15)
x = (8*15)/5 = 24
ANSWER B
Answer: (B) 24
Question: Two ants, Arthur and Lily, have discovered a picnic and are bringing crumbs back to the anthill. Lily makes twice as many trips and carries one and a half times as many crumbs per trip as Arthur. If Arthur carries a total of a crumbs to the anthill, how many crumbs will Lily bring to the anthill, in terms of a?
(A) a/2
(B) a
(C) 3a/2
(D) 2a
(E) 3a
Rationale: Lets do it by picking up numbers. Let Arthur carry 2 crumbs per trip, this means Lily carries 3 crumbs per trip. Also let Arthur make 2 trips and so Lily makes 4 trips.
Thus total crumbs carried by Arthur (a) = 2 x 2 = 4, total crumbs carried by Lily = 3 x 4 = 12. 12 is 3 times 4, so E
Answer: (E) 3a
Question: What will come in place of (a) in the following expression?
a - 996.21 + 498.05 = 215.50 – 425.01
(A) 288.64
(B) 888.6
(C) 888.67
(D) 83.65
(E) 288.65
Rationale: Explanation:
a - 996.21 + 498.05 = 215.50 - 425.01
a = 288.65
ANSWER: E
Answer: (E) 288.65
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2 : 5
(B) 1 : 5
(C) 3 : 5
(D) 4 : 5
(E) None of these
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2 : 5
ANSWER:A
Answer: (A) 2 : 5
Question: In how many different ways can 3 identical bowls of beef ramen noodles and 3 identical bowls of pork ramen noodles be distributed among 6 women such that each woman receives a bowl?
(A) 442
(B) 4011
(C) 94
(D) 151
(E) 20
Rationale: Approach 1:
1st Woman: 6 has options
2nd Woman: 5 has options…
Therefore, for all women: 6 x 5 x 4 x 3 x 2 = 720 arrangements.
Since the beef bowls are identical, we divide by 3!; Since the pork bowls are identical, we divide by another 3!
So: in all, 720/[ 3! X 3! ] = 20 ways.
(e.g. Answer: E)
Answer: (E) 20
Question: Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age
(A) 77
(B) 30
(C) 66
(D) 55
(E) 44
Rationale: Let the age of younger person is x,
Then elder person age is (x+16)
=> 3(x-6) = (x+16-6) [6 years before]
=> 3x-18 = x+10
=> x = 14.
So other person age is x + 16 = 30
Answer:B
Answer: (B) 30
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
(A) 2.5 sec
(B) 4.25 sec
(C) 5 sec
(D) 12.5 sec
(E) 6 sec
Rationale: Speed = 144 * 5/18 = 40 m/sec
Time taken = 100/40 = 2.5 sec.
ANSWER:A
Answer: (A) 2.5 sec
Question: Richard will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
(A) 5
(B) 6
(C) 9
(D) 24
(E) 26
Rationale: Richard will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row.person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases...A
Answer: (A) 5
Question: The length and breadth of a rectangle is increased by 10% and 25% respectively. What is the increase in the area?
A. 27.5%
(A) 1 1/2
(B) 1 1/6
(C) 1 1/8
(D) 1 1/1
(E) 1 1/4
Rationale: 3/20 * 2 + (2 + x)/5 = 1
x = 1 1/2 days
Answer:B
Answer: (B) 1 1/6
Question: Solve the equation for x : 19(x + y) + 17 = 19(-x + y) - 21?
(A) -1
(B) 77
(C) 8
(D) 3
(E) 2
Rationale: 19x + 19y + 17 = -19x + 19y - 21
38x = -38 => x = -1
Answer: A
Answer: (A) -1
Question: A chemist mixes one liter of pure water with x liters of a 45% salt solution, and the resulting mixture is a 15% salt solution. What is the value of x?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 1
(E) 3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 45%
Concentration of salt in the mixed solution = 15%
The pure solution and the salt solution is mixed in the ratio of --> (45 - 15)/(15 - 0) = 2/1
1/x = 2/1
x = 1/2
Answer: C
Answer: (C) 1/2