mathewhe/aqua_rat huggingface dataset:
Question: Having received his weekly allowance, a student spent 3/5 of his allowance at the arcade. The next day he spent one third of his remaining allowance at the toy store, and then spent his last $0.40 at the candy store. What is this student’s weekly allowance?
(A) $1.20
(B) $1.50
(C) $1.80
(D) $2.00
(E) $2.50
Rationale: Let x be the value of the weekly allowance.
(2/3)(2/5)x = 40 cents
(4/15)x = 40
x = $1.50
The answer is B.
Answer: (B) $1.50
Question: Due to construction, the speed limit along an 15-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A)  5
(B)  8
(C)  9.36
(D)  15
(E)  24
Rationale: Old time in minutes to cross 15 miles stretch = 15*60/55 = 15*12/11 = 16.36
New time in minutes to cross 15 miles stretch = 15*60/35 = 15*12/7 = 25.71
Time difference = 9.36
Answer C)
Answer: (C)  9.36
Question: A certain function f satisfies the equation f(x)+2*f(6-x)=x for all real numbers x. The value of f(1) is
(A) 3
(B) 1
(C) 2
(D) 5
(E) 6
Rationale: Put x =1 ⇒ f(1)+2*f(6-1) = 1 ⇒ f(1) + 2*f(5) = 1
Put x = 5 ⇒ f(5)+2*f(6-5) = 5 ⇒ f(5) + 2*f(1) = 5
Put f(5) = 5 - 2*f(1) in the first equation
⇒ f(1) + 2*(5 - 2*f(1)) = 1
⇒ f(1) + 10 - 4f(1) = 1
⇒ f(1) = 3
Answer: A
Answer: (A) 3
Question: In a group of cows and hens, the number of legs are 14 more than twice the number of heads. The number of cows is
(A) 22
(B) 7
(C) 8
(D) 6
(E) 51
Rationale: Let the number of cows be x and the number of hens be y. Then, 4x + 2y = 2 (x + y) + 14 4x + 2y = 2x + 2y + 14 2x = 14 x = 7.
Answer: B
Answer: (B) 7
Question: Find the value of 3/11 × [(1 + 1/3) (1 + 1/4) …………. (1 + 1/120)] is
(A) 10
(B) 13
(C) 11
(D) 15
(E) 17
Rationale: =3/11 × [(1 + 1/3) (1 + 1/4) ....... (1 + 1/120)]
=3/11 × [4/3 + 5/4 × ........ 121/120]
=3/11 × 4/3 × 5/4 × .... 121/120
=121/11 = 11.
Answer is C.
Answer: (C) 11
Question: If 4 men working 10 hours a day earn Rs. 800 per week, then 9 men working 6 hours a day will earn how much per week?
(A) Rs 840
(B) Rs 1320
(C) Rs 1080
(D) Rs 1680
(E) None of these
Rationale: Explanation :
(Men 4:9) : (Hrs/Day 10:6) :: 800 : x
hence 4 * 10 *x = 9 * 6 * 800
or x = 9*6*800/ 4*10 = 1080
Answer : C
Answer: (C) Rs 1080
Question: Three pipes of same capacity A,B,C can fill a tank in 14 hours. If there are only two pipes C and A of same capacity, the tank can be filled in?
(A) 6
(B) 12
(C) 28
(D) 42
(E) 21
Rationale: The part of the tank filled by three pipes in one hour
= 1/14
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/14= 1/21.
The tank can be filled in 21 hours.
Answer:E
Answer: (E) 21
Question: In one hour, a boat goes 4 km/hr along the stream and 2 km/hr against the stream. The speed of the boat in still water (in km/hr) is:
(A) 3 km/hr
(B) 4 km/hr
(C) 5 km/hr
(D) 6 km/hr
(E) 8 km/hr
Rationale: Upstream relative speed is u + v=4km/hr
Downstream speed is u-v = 2
Where u = speed of boat in still water and v is speed of stream
Then adding two equations u+v + u-v =4+2
2u=6
Finally, u=3.
ANSWER : A
Answer: (A) 3 km/hr
Question: It is required to fix a pipe such that water flowing through it at a speed of 7 metres per minute fills a tank of capacity 220 cubic metres in 10 minutes. The inner radius of the pipe should be :
(A) √2 m
(B) 2 m
(C) 1 m
(D) 1⁄√2 m
(E) None of these
Rationale: Let inner radius of the pipe be r.
Then, 220 = 22⁄7 × r2 × 7 × 10
or r2=220/22×10=1
or r = √1=1 m
Answer C
Answer: (C) 1 m
Question: A = {2, 3, 5, 7, 15}
B = {2, 4, 6, 13}
Two integers will be randomly selected from sets A and B, one integer from set A and one from set B, and then multiplied together. How many different products can be obtained?
(A) 15
(B) 16
(C) 19
(D) 20
(E) 36
Rationale: Step 1: Find out the number of products you get.
5 distinct numbers in set A and 4 distinct in set B so number of products = 5*4 = 20
Step 2: Remove the products that appear more than once.
Notice that 5, 7, 11 and 13 are primes and none of their multiples are in either set. So ignore them. We just need to focus on 2 and 3 of set A and 2, 4 and 6 of set B.
2, 3
2, 4, 6
The only product repeated when you take a number from each set is 12. (3*4 and 2*6) Rest all are distinct.
Answer = 20 - 1 = 16
Note here that the second step will involve manual calculation since it will depend on the specific numbers you have in the two sets.
B
Answer: (B) 16
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 276
(B) 280
(C) 287
(D) 267
(E) 270
Rationale: x*(85/100)
= (480 - x)119/100
x = 280
Answer:B
Answer: (B) 280
Question: n what time will a railway train 60 m long moving at the rate of 36 kmph pass a telegraph post on its way?
(A) 2
(B) 7
(C) 8
(D) 6
(E) 9
Rationale: T = 60/36 * 18/5 = 6 sec
Answer: D
Answer: (D) 6
Question: If the product of the integers w, x, y and z is 840, and if 1 < w < x < y < z, what is the value of w + z?
(A) 10
(B) 11
(C) 16
(D) 18
(E) 21
Rationale: 840= 4* 5 * 6* 7
So w = 4, x = 5, y = 6, z = 7
w + z = 4+ 7= 11
Answer - B
Answer: (B) 11
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 44, the dividend is:
(A) 4884
(B) 5340
(C) 5342
(D) 5345
(E) 5356
Rationale: Divisor = (5 * 44) = 220
= 10 * Quotient = Divisor
=> Quotient = 220/10 = 22
Dividend = (Divisor * Quotient) + Remainder
Dividend = (220 * 22) + 44 = 4884.
A
Answer: (A) 4884
Question: Bullock likes to keep a spare tyre in his car every time. On a certain day, he travels 1, 20,000 km and just to make the most of all the tyres, he changes the tyres between his journey such that each tyre runs the same distance.
What is the distance traveled by each tyre?
(A) 70,000
(B) 60,000
(C) 80,000
(D) 96,000
(E) 10,000
Rationale: The distance traveled by each tyre:
4/5 * 1, 20, 000km = 96,000 km. D
Answer: (D) 96,000
Question: If a person walks at 20 km/hr instead of 10 km/hr, he would have walked 40 km more. The actual distance traveled by him is?
(A) 40 km
(B) 76 km
(C) 18 km
(D) 16 km
(E) 97 km
Rationale: Let the actual distance traveled be x km. Then,
x/10 = (x + 40)/20
10x - 400 =>x = 40 km.
Answer: A
Answer: (A) 40 km
Question: If a man lost 10% by selling oranges at the rate of 10 a rupee at how many a rupee must he sell them to gain 50%?
(A) 6
(B) 8
(C) 7
(D) 4
(E) 2
Rationale: 90% ---- 10
150% ---- ?
90/150* 10 = 6
Answer: A
Answer: (A) 6
Question: Marge has 3 pumps for filling her swimming pool. When all 3 pumps work at their maximum rates, the swimming pool is filled in 56 minutes. Pump 1's maximum rate is twice the maximum rate of pump 2 and four times the maximum rate of pump 3. How long would it take Marge to fill the pool if she used only pump 2 at its maximum rate ?
(A) 3hrs, 16mins
(B) 6hrs, 32mins
(C) 7hrs, 12mins
(D) 13hrs, 4mins
(E) 14hrs, 24mins
Rationale: The rate of pump 1 = 4x job/minute.
The rate of pump 2 = 2x job/minute.
The rate of pump 3 = x job/minute.
Given that x+2x+4x=1/56 --> x=1/392 --> (time) = (reciprocal of rate) = 392 minutes x/2= 196 = 3 hrs 16 minutes.
Answer: A
Answer: (A) 3hrs, 16mins
Question: A watch which gains uniformly, is 6 min. slow at 8 o'clock in the morning Sunday and it is 6 min. 48 sec. fast at 8 p.m. on following Sunday. When was it correct?
(A) 20 min past 7 pm on Tuesday
(B) 20 min. past 7 p.m.on Wednesday
(C) 20 min. past 7 p.m. on Thursday
(D) 20 min. past 7 p.m. on Friday
(E) None of these
Rationale: Explanation :
Time from 8 a.m. on Sunday to 8 p.m. on following Sunday = 7 days 12 hours = 180 hours
The watch gains (5 + 29/5) min. or 54/5 min. in 180 hrs.
Now 54/5 min. are gained in 180 hrs.
5 min. are gained in (180 x 5/54 x 5) hrs = 83 hrs 20 min. = 3 days 11 hrs 20 min.
Watch is correct 3 days 11 hrs 20 min. after 8 a.m. of Sunday.
It will be correct at 20 min. past 7 p.m. on Wednesday.
Answer : B
Answer: (B) 20 min. past 7 p.m.on Wednesday
Question: At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score Q of team B?
(A) 1)8
(B) 2)10
(C) 3)20
(D) 4)40
(E) 5)80
Rationale: A to B = 3 : 4
So, on doubling we get 6 : 4
A to C = 3 : 5
So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20
So final ratio = 6 : 4 : 20.
If 20x = 40
4x = 8
Hence, answer is A
Answer: (A) 1)8
Question: If a bus moving at the speed of y km/hr travels a distance of x km, which of the following cannot be equal to the distance traveled?
(A) y-x km
(B) y/2 km
(C) (y-x)/2 km
(D) x/y km
(E) x-y km
Rationale: This question can be solved by TESTing VALUES, but there's a particular pattern that you have to recognize to make the workeasy.
We're not really limited by anything in this question, so X and Y can be anything. Under normal circumstances, I won't TEST the number 1 in PS questions (as it often leads to duplicate answers), but here it's a great option (since we're looking to eliminate 4 answers, multiple TESTs are going to be likely anyway).
We're given information on speed (y km/hour) and distance (x km). We're asked which of the 5 answer choices CANNOT be the distance traveled.
IF....
Y = 2 and X = 1
Answers A (2-1 = 1) and B (2/2 = 1) are POSSIBLE. Eliminate A and B.
IF....
Y = 3 and X = 1
Answer C ([3-1]/2 = 1) is POSSIBLE. Eliminate C.
IF....
Y = 1 and X = 1
Answer D (1/1 = 1) is POSSIBLE. Eliminate D.
Final Answer:
E
Answer: (E) x-y km
Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?
(A) 6
(B) 4
(C) 24.5
(D) 20.5
(E) 12.5
Rationale: Explanatory Answer
9, 40 and 41 is Pythagorean triplet. So, the triangle is right angled.
Key property about right triangles
In a right angled triangle, the radius of the circle that circumscribes the triangle is half the hypotenuse.
In the given triangle, the hypotenuse = 41.
Therefore, the radius of the circle that circumscribes the triangle = 41/2 = 20.5 units.
Choice D
Answer: (D) 20.5
Question: When is |x-7| = 7-x?
(A) x>7
(B) x<7
(C) x=7
(D) x<0
(E) x<=7
Rationale: When is |x-7| = 7-x?
Choice A: X=7, it is true but X cannot be always 7
Choice B: X=0, it is also true, but X cannot be always 0
Choice C: X>7, it is false, for e.g. X=6, then one side of equation is 2 and the other side is -2
Choice D: X<=7, this choice encapsulate Choice A, Choice B and for all other conditions and is true for above said equation. Hence the answer choice is E.
Answer: (E) x<=7
Question: A machine, working at a constant rate, manufactures 72 staplers in 28 minutes. How many staplers does it make in 1 hr 52 min?
(A) 268
(B) 262
(C) 300
(D) 288
(E) 250
Rationale: Change 1 hr 52 min to 112 min. For this, we need to set up a simple proportion of staplers per time 72/28= S/112.
The absolutely worst thing you could do at this point in the problem is to cross-multiply. That would be a supremely unstrategic move. We can cancel the common factor of 28 in the two denominators.
72/28*28 = S/112*28
72/1 = S/4
S = 4* 72
S = 288
The machine would be 288 staplers in 1 hr 52 min.
Answer:D
Answer: (D) 288
Question: Virat buys an old car for Rs. 50000 and spends Rs. 2000 on its repairs. If he sells the car for Rs. 62000, his gain percent is:
(A) 19.23%
(B) 11 (1/9) %
(C) 12.1 %
(D) 12%
(E) None of these
Rationale: Explanation:
C.P. = Rs. (50000 + 2000) = Rs. 52000
S.P. = Rs. 62000.
Gain% = ( (10000 / 52000) * 100 ) % = 19.23%
ANSWER A
Answer: (A) 19.23%
Question: If a, r, and c are consecutive even integers and a < r < c, all of the following must be divisible by 4 EXCEPT
(A) a + c
(B) r + c
(C) ac
(D) (bc)/2
(E) (abc)/4
Rationale: I did get the correct answer within 80 seconds and it was not by luck either. I did not pick numbers but just used the concept stated by Ian.
The 3 numbers can be written as
a, (a + 2)(a + 4).
If 'a' is divisible by 4, then even 'c' or 'a + 4' is divisible by 4. However, is 'b' is divisible by 4, then both 'a' and 'a + 4' are still divisible by 2.
A - (a + c) = a + (a + 4) = 2a + 4 = 2(a + 2) = 2b. 2b will always be divisible by 4 even if 'b' is not divisible by 4. Reason: 'b' already has a prime factorization of at least a '2'. Hence '2b' has two 2s.
C - ac = a(a+4). If, as stated above, one of them is divisible by 4, then the product is divisible. If both of them are not divisible by 4, then the product is still divisible by 4 because of the presence of two 2s again in the prime factorization.
D - bc/2 = (a + 2)(a + 4)/2. Either b or c is divisible by 2. Hence, if we assume that b is divisible by 2 and not divisible by 4, then it leaves us just one possibility. Is c divisible by 4? It has to be because c is the next consecutive even integer.
E - abc/4 = a(a + 2)(a + 4)/4. One of these integers is divisible by 4 already. If we again assume 'b' to be that integer divisible by 4, then we are left with the question - Is a(a + 4) divisible by 4? This is the same as option C.
B - r + c = (a + 2) + (a + 4) = 2a + 6 = 2(a + 3). (a + 3) will never be divisible by 2 because it is an odd integer. Hence, 2(a + 3), although divisible by 2, will not be divisible by 4 because it has just one 2 in its prime factorization.
As a whole, whether you choose numbers (2, 46 being the easiest) or solve conceptually, the answer is still easily obtainable within 2 minutes.B
Answer: (B) r + c
Question: An investor bought 200 shares of stock in ABCD company in 1990. By 1992, the investment was worth only 2/3 of its original value. By 1995, the 200 shares were worth only 2/5 of their value in 1990. By what percent did the value of the investment drop from 1992 to 1995?
(A) 16 2/3%
(B) 25%
(C) 40%
(D) 50%
(E) 66 2/3%
Rationale: Let price of each share in 1990 = X.
Total cost in 1990 = 200X
Now Price in 1992 = 2/3 * 200X = 400/3 * X
Now price in 1995 = 2/5 *200X= 80X
%Change in 1995 from 1992 = [(400/3* X -80X) / (400/3 *X) ] *100 = 40%
Answer C
Answer: (C) 40%
Question: In a group of 6 boys&4 girls a Committee of 4 persons is to be formed. In how many different ways can it be done so that the committee has at least 1girl?
(A) 110
(B) 130
(C) 145
(D) 195
(E) 200
Rationale: The committee of 4 persons is to be so formed that it has at least 1 woman The different ways that we can choose to form such a committee are:
(i) lw. 3 m in t 6X5X4' x 6C3 = 4x — — 80 3X2X1
x 6c2 =42:: x 26:: = 90 (ii) 2w. 2 m in °C2 (iii) 3w. 1 m in 4C3 x 6C1 = 4 x 6 = 24 (iv) 4w in 6C4 = 1 Total no. of different ways in which a committee of 4 persons can be formed so that it has at least one woman. = 80 + 90 + 24 + 1 = 195
D
Answer: (D) 195
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 26 ways
(B) 19 ways
(C) 30 ways
(D) 76 ways
(E) 15 ways
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Answer: (C) 30 ways
Question: we have two cubes which are joined to each other covering one face of each. and remaining faces of both are colored with the different colors.then the first cube is cut into 8 smaller cubes and another in 27 smaller cubes. what is the total number of faces having no color?
(A) 141
(B) 142
(C) 143
(D) 144
(E) 145
Rationale: each cube having 6 faces
for each cube 5 faces has color and one face for each has not
1st cube divided into 8 smaller cubes so num of faces = 8*6 = 48
in this 48 faces 5*4 = 20 faces having the color and 28 don't
because if we divided a cube into 2^n smaller cubes (2^3 = 8) then each face of original cube is divided into 2^(n-1) smaller faces (2^2 = 4) [and inner faces also there]
similarly 2nd cube divided into 27 smaller cubes so num of faces = 27*6 = 162
in tiis 162 faces 5*9 = 45 faces having color and 117 don't
total no of faces having no color = 28+117 = 145
ANSWER:E
Answer: (E) 145
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 m2
(B) 50 m2
(C) 53.5 m2
(D) 55 m2
(E) 58 m2
Rationale: 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] m2
= 49 m2. Answer: Option A
Answer: (A) 49 m2
Question: HCF of two numbers is 11 and the product of these numbers is 363, what is the the greater number?
(A) 28
(B) 31
(C) 33
(D) 35
(E) 38
Rationale: The numbers be 11a and 11b
11a × 11b = 363
ab = 3
co-primes with product 3 are (1, 3)
Hence the numbers with HCF 11 and product 363
= (11 × 1, 11 × 3)
= (11, 33)
Numbers are 11 and 33
The greater number = 33
Answer: (C) 33
Question: Sony and Johnny caught 25 fishes. Sony caught four times as many as Johnny. How many fishes did Johnny catch?
(A) 5
(B) 16
(C) 34
(D) 38
(E) 42
Rationale: s+j=25
s=4*j
j=5
ANSWER:A
Answer: (A) 5
Question: Which of the following is closer to (21!+20!)/(21!-20!)?
(A) 49
(B) 36
(C) 25
(D) 16
(E) 1
Rationale: Notice that 21! = (21)(20!), so we can factor out 20! from top and bottom.
(21!+20!)/(21!-20!)=[20!(21+1)]/[20!(21-1)]
= (21+1)/(20-1)
= 22/19
≈ 1
Answer: E
Answer: (E) 1
Question: if a@b = a * b^(1/2) then 2@16 = ?
self made
(A) 2
(B) 6
(C) 3
(D) 8
(E) 4
Rationale: 2* (16)^1/2= 2*4= 8
D is the answer
Answer: (D) 8
Question: If integers ending in zero are excluded, what is the unit digit of the product of the even integers from 802 to 898, inclusive?
(A) 14
(B) 12
(C) 10
(D) 6
(E) 8
Rationale: 802 x 804 x 806 x 808 => unit digit 4
812 x 814 x 816 x 818 => unit digit 4
892 x 894 x 896 x 898 => unit digit 4
So we have 10 numbers ending by 4 to multiply.
Given that 4 x 4 = 16, we have 5 numbers ending by 6 to multiply
Given that 6 x 6 = 36, we have 3 numbers ending by 6 to multiply
So the unit digit is 6
Answer : D
Answer: (D) 6
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
(A) 5/8
(B) 5/9
(C) 5/2
(D) 5/1
(E) 5/6
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer: B
Answer: (B) 5/9
Question: It is given that 2^32 + 1 is exactly divisible by a certain number. Which one of the following is also divisible by the same number W?
(A) a. 2^96 + 1
(B) b. 2^16 - 1
(C) c. 2^16 + 1
(D) d. 7 * 2^33
(E) e. 2^64 + 1
Rationale: a³ + b³ =(a+b)(a² -ab +b²)
Now, let (2^32 + 1) be (a+b)
a³ + b³ = (2^96 + 1)
Now, as mentioned in formula above,
a³ + b³ is always divisible by (a+b)
So any factor of W (a+b) is a factor of (a³ + b³)
Henca A
Answer: (A) a. 2^96 + 1
Question: There are 20 students with an average height of 105 cms in a class. Then 10 students with an average height of 120 cms join the class. What will be the average height of the class now?
(A) 110 cms
(B) 120 cms
(C) 100 cms
(D) 115 cms
(E) 130 cms
Rationale: 20 students average height is 105cms
sum of heights/ 20 =105cms
sum of heights of 20 students= 105*20= 2100
10 students of average height 120 added
so their, sum of 10 students height / 10 = 120
sum of heights of 10 students = 1200cms
By adding heights of 20 and 10 students , 1200+2100 = 3300
average of 30 students = 3300/30 = 110 cms
ANSWER:A
Answer: (A) 110 cms
Question: In how many ways 7 boys and 7 girls can be seated in a row so that boys and girls are alternate?
(A) 50803200
(B) 50328000
(C) 50003280
(D) 50703200
(E) 50603200
Rationale: number of ways = 2*7!*7! = 50803200
Answer is A
Answer: (A) 50803200
Question: √{(1.5)(10^9)} is closest to which of the following?
(A) 5,000
(B) 20,000
(C) 40,000
(D) 100,000
(E) 200,000
Rationale: √{(1.5)(10^9)} = √{(15)(10^8)} = √(15)√(10^8) = (√15) * 10,000 which is almost 40,000.
The answer is C.
Answer: (C) 40,000
Question: The football association pays $2000 out of $8000 it owes to refrees. Then it pays $6000 out of the $12000 owes for the year to players.
How much did the ratio of payments made to monies owed increase?
(A) A) 75%
(B) B)100 %
(C) C)1%
(D) D) 50%
(E) E) 25%
Rationale: Ratio in 1st case 2000:8000(1/4)
Ratio in second case 6000/12000 (2/4)
percentage increase is (difference/initial quantity)*100
(1/4)/(2/4 )* 100= 100%
Correct option is B
Answer: (B) B)100 %
Question: 8 boys complete a work in 14 days . In how many days will 14 boys complete that work?
(A) 14 days
(B) 7 days
(C) 8 days
(D) 6 days
(E) 5 days
Rationale: Explanation:
1 boy 1 day work = 14 × 8,
14 boys complete the work in 14 × 8/14= 8 days
Answer: Option C
Answer: (C) 8 days
Question: The side of a square is increased by 20% then how much % does its area increases?
(A) 44.00 %
(B) 45.25 %
(C) 48.75 %
(D) 50.00 %
(E) 40.00 %
Rationale: a = 100 a2 = 10000
a = 120 a2 = 14400
----------------
10000 --------- 4400
100 -------? => 44.00 %
Answer:A
Answer: (A) 44.00 %
Question: A room of 5m 44cm long and 3m 74cm broad is to be paved with squre tiles. Find the least number of squre tiles required to cover the floor.
(A) 233
(B) 877
(C) 279
(D) 176
(E) 291
Rationale: Explanation:
area of the room = 544 * 374 sq cm
size of largest square tile = H.C.F of 544cm and 374cm= 34cm
area of 1 tile = 34*34 sq cm
no. of tiles required = (544*374) / (34 * 34) = 176
Answer: D) 176
Answer: (D) 176
Question: If the price of a commodity is decreased by 20% and its consumption is increased by 20%, what will be the increase or decrease in expenditure on the commodity?
(A) 4% increase
(B) 4% decrease
(C) 8% increase
(D) 8% decrease
(E) None
Rationale: Solution: Let the initial expenditure on the commodity be Rs. 100.
Now, the price decreases by 20%,
Current Price = (100 - 20% of 100) = Rs. 80.
Same time due to decrement in price 20% consumption has been increased. So,
Current expenses on commodity = (80 + 20% of 80)= Rs. 96.
Here, the initial expenditure was Rs. 100 which became 96 at the end, it means there is 4% decrement in the expenditure of the commodity.
Mind Calculation Method:
100===20%↓(Decrement in Price)===>80===20%↑(Increment in Consumption)===>96.
Thus, there is a decrement of 4%.
Answer: Option B
Answer: (B) 4% decrease
Question: What is the present worth of Rs. 122 due in 2 years at 5% simple interest per annum?
(A) Rs.154.32
(B) Rs.121.42
(C) Rs. 112
(D) Rs.110.99
(E) Rs.120.99
Rationale: Let the present worth be Rs. x. Then,
S.I. = (122 - x)
(x * 5 * 2) / 100 = (122 - x)
10x = 12200 - 100x
110x = 12200 => x = 110.99
ANSWER:D
Answer: (D) Rs.110.99
Question: For any positive integer p, the sum of the first p positive integers equals p(p+1)/2 . If q and p are positive integers and q > p, what is the sum of all the integers between q and p, inclusive?
(A)  q(q+1)/2 + p(p+1)/2
(B)  q(q+1)/2 - p(p-1)/2
(C)  q(q+1)/2 - p(p+1)/2
(D)  q(q+1)/2 + p(p-1)/2
(E)  q(p+1)/2 - p(q-1)/2
Rationale: The sum of all the integers between q and p,inclusiveis the sum of the first q positive integersminusthe sum of the first p-1 positive integers.
The sum of the first q positive integers is q(q+1)/2;
The sum of the first p-1 positive integers is (p-1)p/2;
Therefore the answer is q(q+1)/2 - (p-1)p/2.
Answer: B.
Answer: (B)  q(q+1)/2 - p(p-1)/2
Question: The average age of applicants for a new job is 31, with a standard deviation of 5. The hiring manager is only willing to accept applications whose age is within one standard deviation of the average age. What is the maximum number of different ages of the applicants?
(A) 11
(B) 14
(C) 15
(D) 18
(E) 30
Rationale: within one standard deviation of the average age means 31 +/- 7
26--31--36
number of dif.ages -26 27 28 29 30 31 32 33 34 35 36
total=11
A
Answer: (A) 11