mathewhe/aqua_rat huggingface dataset:
Question: Lamp A flashes every 6 seconds, Lamp B flashes every 8 seconds, Lamp C flashes every 10 seconds. At a certain instant of time all three lamps flash simultaneously. During the period of 10 minutes after that how many times will exactly two lamps flash? (Please include any flash of exactly two lights which occurs at the 10 minute mark.)
(A) 41
(B) 42
(C) 43
(D) 44
(E) 45
Rationale: 10 minutes is 600 seconds.
Lamp A and Lamp B will flash together every 24 seconds.
600/24=25.
In the time period, Lamp A and Lamp B will flash together 25 times.
Lamp A and Lamp C will flash together every 30 seconds.
600/30=20.
In the time period, Lamp A and Lamp C will flash together 20 times.
Lamp B and Lamp C will flash together every 40 seconds.
600/40=15.
In the time period, Lamp B and Lamp C will flash together 15 times.
All three lights will flash together every 2*2*2*3*5=120 seconds.
600/120=5.
We have counted these triple flashes three times, so we need to subtract three times the number of times that all three lights flash together.
The number of times that exactly two lights flash together is 25+20+15-15=45 times.
The answer is E.
Answer: (E) 45
Question: At the recent downhill mountain bike race 4 entrants entered a challenging slalom event. Prem came first. The entrant wearing no 2 wore red. whereas kian did not wear yellow. the loser wore blue and rahul wore no 1.Sanjay beat rahul and the person who came second wore no 3.te entrant in yellow beat the entrant in green. Only one of the entrant s wore the same number and the final position. Determine who finished 3rd, the no and the color they wore?
(A) Rahul 1 green
(B) rahul 2 red
(C) Kiran 4 blue
(D) Kiran 7 blue
(E) none of these
Rationale: the names are prem, sanjay, rahul, kian
colors are red,yellow,green,blue
since prem came 1st and sanjay beat rahul so, given that sanjay came 2nd, wore no 3, yellow color
and rahul wore no 1, green color, came 3rd
hence,
name position wore t-shirt no color
prem 1 2 red
sanjay 2 3 yellow
rahul 3 1 green
kian 4 (1,2,3) blue
ANSWER:A
Answer: (A) Rahul 1 green
Question: Find the area of a parallelogram with base 32 cm and height 18 cm?
(A) 576 cm2
(B) 384 cm2
(C) 672 cm2
(D) 267 cm2
(E) 286 cm2
Rationale: Area of a parallelogram
= base * height
= 32 * 18
= 576 cm2
Answer: A
Answer: (A) 576 cm2
Question: Souju's age is 115% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age?
(A) 56 years
(B) 72 years
(C) 56 years
(D) 66 years
(E) 76 years
Rationale: Let the age before 10 years =x. Then,
115x/100=x+10
⇒115x=100x+1000
⇒x=1000/15=66
Present age =x+10=66+10=76
ANSWER:E
Answer: (E) 76 years
Question: On the first of the year, James invested x dollars at Proudstar bank in an account that yields 0.5% in interest every quarter year. At the end of the year, during which he made no additional deposits or withdrawals, he had y dollars in the account. If James had invested the same amount in an account which pays interest on a yearly basis, what must the interest rate be for James to have y dollars at the end of the year?
(A) 2.04%
(B) 4.12%
(C) 5%
(D) 8.25%
(E) 10%
Rationale: Per quarter, interest = 0.5% So for a year, interest = 2% Due to quarter cumulation, effective yield (YTM) would be slight higher than 2% Answer = 2.04% =ANSWER:A
Answer: (A) 2.04%
Question: A set consists of 15 numbers, all are even or multiple of 5. If 8 numbers are even and 10 numbers are multiple of 5, how many numbers is multiple of 10?
(A)  0
(B)  1
(C)  2
(D)  3
(E)  5
Rationale: {Total} = {Even} + {Multiple of 5} - {Both} + {Nether}.
Since{Neither}=0(allare even or multiple of 5) then:
15 = 8 + 10 - {Both} + 0;
{Both}=3(so 1 number is both even AND multiple of 5, so it must be a multiple of 10).
Answer: D.
Answer: (D)  3
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.20 per kg. What will be his gain percent?
(A) 8 1/7 %
(B) 2 1/3 %
(C) 3 1/3 %
(D) 8 1/8 %
(E) 8 1/9 %
Rationale: C.P. of 1 kg = 420/70 = Rs. 6
S.P. of 1 kg = Rs. 6.20
Gain % = 0.20/6 * 100 = 10/3
= 3 1/3 %
Answer:C
Answer: (C) 3 1/3 %
Question: What should be the least number to be added to the 51234 number to make it divisible by 9?
(A) 12
(B) 17
(C) 18
(D) 77
(E) 26
Rationale: Explanation:
The least number to be added to the numbers to make them divisible by 9 is equal to the difference of the least multiple of 9 greater than the sum of the digits and sum of the digits.
Sum of digits = 15.
Nearest multiple of 9 greater than sum of digits = 18.
Hence 3 has to be added.
Answer: C
Answer: (C) 18
Question: A set of numbers has the property that for any number t in the set,t+2 is in the set. If -2 is in the set, which of the following must also be in the set? I. -3 II. 1 III. 4
(A) II only
(B) I,III only
(C) III only
(D) II,III only
(E) I only
Rationale: question is asking for must be there elements.
According to the question if t is there t+2 must be there.
if -2 is the starting element the sequence is as follows.
S ={-2,0,2,4,6....}
if -2 is not the starting element the sequence is as follows
S = {...-4,-2,0,2,4,6...}
By observing the above two sequences we can say that 4 must be there in set S.
Answer : C
Answer: (C) III only
Question: After allowing a discount of 15% on the marked price, the selling price is Rs. 6800 for an article. If it was sold at marked price, there would have been a profit of 60%. The cost price of the article is?
(A) Rs.2989
(B) Rs.5029
(C) Rs.5000
(D) Rs.5197
(E) Rs.5029
Rationale: Given SP = Rs. 6800
Marked price = [SP(100)]/(100 - d%) = (6800 * 100)/(100 - 15)
= Rs. 8000
If SP = Rs. 8000, profit
60%
CP = [SP(100)]/(100 + 60)
= (8000 * 100)/160
= Rs.5000
Answer: C
Answer: (C) Rs.5000
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 90%
(B) 50%
(C) 60%
(D) 70%
(E) 80%
Rationale: circumference of A = 2(pie)r = 8 so r = 4/pie
volume = pie(4/pie)^2*10 = 160/pie
circumference of B = 2(pie)r = 10 so r = 5/pie
volume = pie(5/pie)^2*8 = 200/pie
so ratio of capacities = 160/200 = 0.8
so capacity of A will be 80% of the capacity of B
ANSWER:E
Answer: (E) 80%
Question: If x, y, and z are positive integers, and 2x = 5y = 7z, then the least possible value of x + y + z is
(A) 15
(B) 28
(C) 37
(D) 42
(E) 59
Rationale: Take LCM of 2,5 and 7 = 70
Now 2x = 70 => x =35
5y = 70 => y = 14
7z = 70 => z =10
35+14+10 = 59.
Option E.
Answer: (E) 59
Question: What is the least number of squares tiles required to pave the floor of a room 2 m 42 cm long and 1 m 76 cm broad?
(A) 88
(B) 82
(C) 84
(D) 44
(E) 54
Rationale: Length of largest tile = H.C.F. of 242 cm and 176 cm = 22 cm.
Area of each tile = (22 x 22) cm2.
Required number of tiles =242 x 176/(22^2)= 88.
ANSWER:A
Answer: (A) 88
Question: A money lender finds that due to a fall in the annual rate of interest from 8% to 7 ¾ % his yearly income diminishes by Rs.61.50. his capital is
(A) 22378
(B) 3778
(C) 24600
(D) 27888
(E) 12771
Rationale: Explanation:
Capital = Rs.x , then
x = 24600
Answer: C) Rs.24600
Answer: (C) 24600
Question: A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and black. How far is the place?
(A) 2.89
(B) 2.88
(C) 2.82
(D) 2.84
(E) 2.83
Rationale: M = 6
S = 1.2
DS = 6 + 1.2 = 7.2
US = 6 - 1.2 = 4.8
x/7.2 + x/4.8 = 1
x = 2.88
Answer:B
Answer: (B) 2.88
Question: A train speeds past a pole in 15 seconds and a platform 100 m long in 25 seconds. Its length is?
(A) 272
(B) 111
(C) 822
(D) 150
(E) 379
Rationale: Let the length of the train be x meters and its speed be y m/sec.
They, x / y = 15 => y = x/15
x + 100 / 25 = x / 15
x = 150 m.
Answer:D
Answer: (D) 150
Question: Indu gave Bindu Rs.2500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
(A) 1
(B) 2
(C) 7
(D) 4
(E) 9
Rationale: 2500 = D(100/4)2
D = 4
Answer:D
Answer: (D) 4
Question: x = y - (1/y), where x and y are both > 0. If the value of y is doubled in the equation above, the value of x will
(A) decrease
(B) stay the same
(C) increase four fold
(D) just more than double
(E) increase to more than five times
Rationale: Alternate approach
Plug in some values of y > 0
Let y = 10
So, x = y - (1/y)
Or, x = 10 - (1/10) = 9.9
Let y = 20
So, x = y - (1/y)
Or, x = 20 - (1/20) =>19.95
So, x increases from 9.9 to 19.95
Hence the number increases 2 times, thus the correct answer will be (D)
Answer: (D) just more than double
Question: A tourist purchased a total of $3,500 worth of traveler’s checks in $10 and $50 denominations, During the trip the tourist cashed 7 checks and then lost all of the rest. If the number of $10 checks cashed was one more or one less than the number of $50 checks cashed, what is the minimum possible value of the checks that were lost?
(A) $1,430
(B) $2,310
(C) $2,290
(D) $3,270
(E) $4,150
Rationale: Let the number of $10 checks cashed beT
Let the number of $50 checks cashed beF
7 checks cashed;
T+F=7
Now; T can be F+1 OR T can be F-1
Let's check both conditions;
T=F+1
T+F=7
F+1+F=7
2F=6
F=3
T=4
Value cashed = 3*50+4*10=150+40=$190
Let's check the other condition as well;
T=F-1
T+F=7
F-1+F=7
2F=8
F=4
T=3
Value cashed = 4*50+3*10=200+30=$230
The more money he cashes, the less loss he incurs. Thus, we must consider the latter case.
Value cashed = $230
Value lost = 3000-230 = $3270
Ans:D
Answer: (D) $3,270
Question: Dany bought a total of 20 game cards some of which cost $0.25 each and some of which cost $0.15 each. If Dany spent $4.2 to buy these cards, how many cards of each type did he buy?
(A) 2
(B) 3
(C) 5
(D) 8
(E) 13
Rationale: Let X be the number of cards that cost $0.25 each and Y the number of cards that cost $0.15 each. The total number of cards is 20. Hence
X + Y = 20
If X is the number of cards at $0.25, then the X cards cost
0.25 X
If Y is the number of cards at $0.15, then the Y cards cost
0.15 Y
The total cost of the X cards and the the Y cards is known to be $4.2 and also given by
0.25 X + 0.15 Y = 4.2
We now need to solve the system of equations
X + Y = 20
0.25 X + 0.15 Y = 4.2
The first equation gives Y = 20 - X. Substitute y by 20 - x in the second equation and solve
0.25 X + 0.15 (20 - X) = 4.2
X(0.25 - 0.15) + 3 = 4.2
0.1 X = 1.2
X = 12 and Y = 20 - 12 = 8
correct answer D
Answer: (D) 8
Question: What is vasu salary if salary of vasu is more than rajan salary working in same company i)vasu salary is 100 more than rajan salary. ii)rajan found 2000 allowns which is 50 less than vasu. (iii)basic salry of rajan is 1000.
(A) only i is required
(B) i & ii is required
(C) i& iii is required
(D) i&ii&iii is required
(E) none of these
Rationale: i and iii is enough
ANSWER:B
Answer: (B) i & ii is required
Question: The distance light travels in one year is approximately 5,850,000,000,000 miles. The distance light travels in 100 years is
(A) A) 587 × 108 miles
(B) B) 587 × 1010 miles
(C) C) 587 × 10-10 miles
(D) D) 585 × 1012 miles
(E) E) 587 × 10-12 miles
Rationale: The distance of the light travels in 100 years is:
5,850,000,000,000 × 100 miles.
= 585,000,000,000,000 miles.
= 585 × 1012 miles.
The answer is (D)
Answer: (D) D) 585 × 1012 miles
Question: A box contains four nickel coins, of which two coins have heads on both their faces, one coin has tail on both its faces and the fourth coin is a normal one. A coin is picked at random and then tossed. If head is the outcome of the toss, then find the probability that the other face (hidden face) of the coin tossed is also a head.
(A) 3/5
(B) 2/5
(C) 4/5
(D) 1/5
(E) 3/4
Rationale: There are four ways (2 heads in one two-headed coin and 2 heads in the other two-headed coin)
How many ways can you get heads from this entire set of coins? There are five ways (four as identified above and one from the normal coin)
Therefore probability = (number of ways to get heads from a two-headed coin)/(number of ways to get heads from any coin)
= 4/5
C
Answer: (C) 4/5
Question: The owner of a furniture shop charges his customer 60% more than the cost price. If a customer paid Rs. 1000 for a computer table, then what was the cost price of the computer table?
(A) 750
(B) 650
(C) 625
(D) 115
(E) 400
Rationale: CP = SP * (100/(100 + profit%))
= 1000(100/160) = Rs. 625.
Answer: B
Answer: (B) 650
Question: If x is an integer and 3.134 × 10^x is less than 31,000 what is the greatest possible value for x?
(A) 7
(B) 6
(C) 5
(D) 4
(E) 3
Rationale: If x=4
3.134 × 10^4 = 31340 > 31000
So, x = 3
Answer : E
Answer: (E) 3
Question: For each hour of production, a certain factory requires 1 assembly line worker for every 25 units to be produced in that hour. The factory also requires 12 managers regardless of the number of units to be produced. Which of the following expressions represents the total number of assembly line workers and managers that this factory requires to produce 75N in one hour, where N is a positive integer?
(A) 12 + 50N
(B) 12 + 3N
(C) 62N
(D) 37N
(E) 25
Rationale: 25 units = 1 worker;
75N units = 75N/25 = 3N workers.
So, the answer is 3N workers plus 12 managers.
Answer: B.
Answer: (B) 12 + 3N
Question: calculate the time required to become sum 2 times of itself at rate of 10%.
(A) 5year
(B) 15year
(C) 10year
(D) 8year
(E) 12year
Rationale: if sum become 2 time then simple interest equal to x.
x=x*10*t/100
t=100/10=10year
answer C
Answer: (C) 10year
Question: find 3 consecutive odd integers, all less than 100, such that the sum of their squares forms a Unidigit (that is, all its digits are the same). Thus, for integer abc, a^2 + b^2 +c^2 equals a Unidigital.
(A) 39,43,45
(B) 43,45,47
(C) 45,47,49
(D) 41,43,45
(E) 41,43,47
Rationale: If numbers are x,x-2,x+2, then
x^2+(x+2)^2 =(x-2)^2 = x^2+2x^2+8 = 3x^2+8
Now 3x^2+8 should be unidigital.
checking different combinations , we get
x=43.
so numbers are 41,43,45
ANSWER:D
Answer: (D) 41,43,45
Question: A train crosses a bridge of length 1500 m in 70 seconds and a lamp post on the bridge in 20 seconds. What is the length of the train in metres?
(A) 375 m
(B) 750 m
(C) 250 m
(D) 600 m
(E) 300 m
Rationale: Let Length of Train = L
Case-1: Distance = 1500+L (While crossing the bridge)
Time = 70 Seconds
i.e. Speed = Distance / Time = (1500+L)/70
Case-2: Distance = L (While passing the lamp post)
Time = 20 Seconds
i.e. Speed = Distance / Time = (L)/20
But Since speed has to be same in both cases so
(1500+L)/70 = (L)/20
i.e. 1500 + L = 3.5 L
i.e. 2.5L = 1500
i.e. L = 600
Answer: option D
Answer: (D) 600 m
Question: A train passes a station platform in 55 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
(A) 180 m
(B) 525 m
(C) 240 m
(D) 320 m
(E) None
Rationale: Sol.
Speed = [54 * 5/18] m/sec = 15 m/sec.
Length of the train = (15 * 20) m = 300 m.
Let the length of the platform be x metres.
Then, x + 300 / 55 = 15 ⇔ x + 300 = 825 ⇔ x = 525 m.
Answer B
Answer: (B) 525 m
Question: The salary of a typist was at first raised by 10% and then the same was reduced by 5%. If he presently draws Rs.1045.What was his original salary?
(A) 28788
(B) 2788
(C) 1000
(D) 2877
(E) 28881
Rationale: X * (110/100) * (95/100) = 1045
X * (11/10) * (1/100) = 11
X = 1000
Answer: C
Answer: (C) 1000
Question: 1 + 1 ÷ {1 + 1 ÷ (1 + 1/3)} = ?
(A) 1 1/3
(B) 1 4/7
(C) 1 1/8
(D) 1 2/3
(E) None
Rationale: Answer
Given expression = 1 + 1 ÷ {1 + 1 ÷ (1 + 1/3)}
= 1 + 1 ÷ { 1 + 1 ÷ 4/3}
= 1 + 1 ÷ { 1 + 3/4}
= 1 + 1 ÷ 7/4
= 1 + 1 x 4/7
= 1 + 4/7
= 1 4/7
Correct Option: B
Answer: (B) 1 4/7
Question: If the sum of three consecutive even numbers is 48 more than the average of these numbers, then the largest of these numbers is?
(A) 20
(B) 24
(C) 22
(D) 26
(E) 27
Rationale: Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 48
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 144
9x + 18 = 3x + 150
6x = 132
x = 22
Therefore, the largest number is 26.
ANSWER D
Answer: (D) 26
Question: A basketball player succeeds with 60% of her free throws. If she has a set of three free throws, what is the probability that she succeeds at least once?
(A) 0.856
(B) 0.872
(C) 0.936
(D) 0.952
(E) 0.985
Rationale: P(missing all 3 free throws) = 0.4^3 = 0.064
P(succeeding at least once) = 1 - 0.064 = 0.936
The answer is C.
Answer: (C) 0.936
Question: A five-character password consists of three letter of the alphabet and two different digits between 0 and 9, inclusive. The letter must appear as the second or third character of the password. How many different passwords are possible?
(A) 225,040
(B) 18,443,720
(C) 26,337,000
(D) 28,337,440
(E) 28,473,120
Rationale: 5 character password: DLDLL
First digit can be chosen in 10 ways.
The letter can be chosen in 26 ways.
Next digit can be chosen in 9 ways.
The letter can be chosen in 25 ways.
The letter can be chosen in 24 ways.
This gives us 10*26*9*25*24ways
Now, the letter can also be DDLD so there will be another 10*9*26*25*24 ways
Total = 10*26*9*25*24*2 = 28,473,120 ways
E
Answer: (E) 28,473,120
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad?
(A) 814
(B) 820
(C) 842
(D) 844
(E) 848
Rationale: Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517×902)/ (41×41) = 814
answer :A
Answer: (A) 814
Question: The sector of a circle has radius of 21 cm and central angle 135o. Find its perimeter?
(A) 91.5 cm
(B) 11.5 cm
(C) 91.8 cm
(D) 92.5 cm
(E) 99.5 cm
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (135/360 * 2 * 22/7 * 21) + 2(21)
= 49.5 + 42
= 91.5 cm
Answer:A
Answer: (A) 91.5 cm
Question: A jogger is running at 9 kmph alongside a railway track in 240 meters ahead of the engine of a 120 meters long train . The train is running at 45 kmph in the same direction. how much time does it take for the train to pass the jogger?
(A) 46 seconds
(B) 36 seconds
(C) 38 seconds
(D) 26 seconds
(E) 18 seconds
Rationale: Distance = 240+ 120 = 360 m
speed = 36 km/hr = 36×10/36 = 10 m/s
Time = distance/speed = 360/10 = 36 seconds
answer : B
Answer: (B) 36 seconds
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 56?
(A) 3944
(B) 920
(C) 3808
(D) 6928
(E) 3729
Rationale: Explanation:
Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 56 = Rs. 3808.
Answer: Option C
Answer: (C) 3808
Question: What is the remainder when (55)(57) is divided by 7?
(A) 1
(B) 2
(C) 3
(D) 5
(E) 6
Rationale: (55)(57) = (56-1)(56+1) = 56^2 - 1 which is 1 less than a multiple of 7.
Then the remainder will be 6.
The answer is E.
Answer: (E) 6
Question: After decreasing 24% in the price of an article costs Rs.684. Find the actual cost of an article?
(A) 218
(B) 777
(C) 900
(D) 2688
(E) 1991
Rationale: CP* (76/100) = 684
CP= 9 * 100 => CP = 900
Answer: C
Answer: (C) 900
Question: A man is 36 years older than his son. In THREE years, his age will be THRICE the age of his son. The present age of this son is
(A) 28 years
(B) 22 years
(C) 18 years
(D) 16 years
(E) 15 years
Rationale: Let's Son age is x, then Father age is x+36.
=> 3(x+3) = (x+36+3)
=> 3x+9 = x+39
=> 2x = 30 years = 15 YEARS
Answer: E
Answer: (E) 15 years
Question: (3 x 10^5) + (2 x 10^3) + (4 x 10^2) =
(A) 302400
(B) 32400
(C) 30240
(D) 3240
(E) 324
Rationale: When you multiply a number by 10 you just add a zero
=> 3 x 10^5 => add 5 zeros => 3 x 10^5 = 300000
=>2 x 10^3 = 2000
=> 4 x 10^2 = 400
=>3 x 10^5 + 2 x 10^3 + 4 x 10^2 = 300000 + 2000 + 400 = 302400
=> answer is A ( 302400)
Answer: (A) 302400
Question: Ravi, Gagan and Nitin are running a business firm in partnership. What is Gagan’s share in the profit earned by them?
I.Ravi, Gagan and Nitin invested the amounts in the ratio of 2 : 4 : 7.
II.Nitin’s share in the profit is Rs. 8750.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: Explanation:
Let us name Ravi, Gagan and Nitin by R, G and N respectively.
I. R : G : N = 2 : 4 : 7.
II. N = 8750..
From I and II, we get:
When N = 7, then G = 4.
When N = 8750, then G = ( 4/7 x 8750) = 5000.
Thus, both I and II are needed to get the answer.
answer is (E).
Answer: (E) Both I and II are necessary to answer
Question: There are C girls in a class, and their average height is M inches. In the same class, there are D boys with an average height of N inches. What is the average height of all the students in the class?
(A) (X + Y)/(M + N)
(B) (M + N)/(X + Y)
(C) (XM + YN)/(M + N)
(D) (CM + DN)/(C+ D)
(E) MN/XY
Rationale: Total height = CM+DN
No of students = C+D
Avg = (CM+DN)/(C+D)
Answer is D
Answer: (D) (CM + DN)/(C+ D)
Question: When x is multiplied by 3, the result is 10 more than the result of subtracting x from 26. What is the value of x?
(A) -4
(B) 9
(C) 11
(D) 13
(E) 22
Rationale: The equation that can be formed is:
3x-10=26-x
or, 4x=36
or, x=9.
B answer.
Answer: (B) 9
Question: A boat can move upstream at 50 kmph and downstream at 100 kmph, then the speed of the current is?
(A) 10
(B) 45
(C) 25
(D) 40
(E) 20
Rationale: US = 50
DS = 100
M = (100- 50)/2
= 25
Answer:C
Answer: (C) 25
Question: A person takes 5hrs 45 min in walking to a place and ridingback. He would have gained 2hrs by riding both ways. The time he would take to walk both ways is?
(A) 5 hours 45 min
(B) 5 hours 55 min
(C) 6 hours 45 min
(D) 7 hours 45 min
(E) 8 hours
Rationale: ----------------------------------------------------------------
Solution 1
----------------------------------------------------------------
Given that time taken for riding both ways will be 2 hours lesser than
the time needed for waking one way and riding back
From this, we can understand that
time needed for riding one way = time needed for waking one way - 2 hours
Given that time taken in walking one way and riding back = 5 hours 45 min
Hence The time he would take to walk both ways = 5 hours 45 min + 2 hours = 7 hours 45 min
D
Answer: (D) 7 hours 45 min
Question: The price of the sugar rise by 25%. If a family wants to keep their expenses on sugar the same as earlier, the family will have to decrease its consumption of sugar by
(A) 25%
(B) 20%
(C) 80%
(D) 75%
(E) None
Rationale: Solution: Let the initial expenses on Sugar was Rs. 100.
Now, Price of Sugar rises 25%. So, to buy same amount of Sugar, they need to expense,
= (100 + 25% of 100) = Rs. 125.
But, They want to keep expenses on Sugar, so they have to cut Rs. 25 in the expenses to keep it to Rs. 100.
Now, % decrease in Consumption,
(25/125)*100 = 20%.
Mind Calculation Method;
100-----25%↑---→125------X%↓---→100.
Here, X = (25/125)*100 = 20%.
Answer: Option B
Answer: (B) 20%
Question: How many integers between 300 and 1100 are there such that their unit digit is odd?
(A) 200
(B) 300
(C) 400
(D) 500
(E) 600
Rationale: There are 800 numbers from 301 to 1100 (inclusive).
Half of the numbers are odd, so there are 400 odd numbers.
The answer is C.
Answer: (C) 400