RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Tough and Tricky questions: Exponents.
If 3^(x+1)*5^(y-1) = 9^x*125^y, then 2x + y =
A.-3/4
B.-2/5
C.-5/2
D.2/5
Answer: C.-5/2
Explanation: Here is my solution.
3^(x+1)*5^(y-1) = 9^x*125^y
Here RHS 9^x*125^y= 3^(2x)*5^(3y)
Equating powers on both sides-->
x+1=2x , thus x=-1 and
y-1=3y giving y=-1/2
So, x+y=-5/2
Option: C
Question: Mixture A is 20 percent alcohol, and mixture B is 50 percent alcohol. If the two are poured together to create a 15 gallon mixture that contains 30 percent alcohol, approximately how many gallons of mixture A are in the mixture?
A.3 gallons
B.4 gallons
C.5 gallons
D.10 gallons
Answer: D.10 gallons
Explanation: Let A = number of gallons on Mixture A in 15 gallon mixture
B = number of gallons on Mixture B in 15 gallon mixture
(20/100)A + (50/100)B= (30/100)(A+B) --1
A+B=15 -- 2
On solving equations 1 and 2 , we get
A=10
B=5
Answer D 10 gallons
Question: A dishonest dealer professes to sell his goods at Cost Price but still gets 20% profit by using a false weight. What weight does he substitute for a kilogram?
A.835 1/3 grams
B.833 1/3 grams
C.833 1/9 grams
D.836 1/3 grams
Answer: B.833 1/3 grams
Explanation: If the cost price is Rs.100, then to get a profit of 20%, the selling price should be Rs.120.
If 120kg are to be sold, and the dealer gives only 100kg, to get a profit of 20%.
How many grams he has to give instead of one kilogram(1000 gm).
120 gm ------ 100 gm
1000 gm ------ ?
(1000 * 100)/120 = 2500/3 = 833 1/3 grams.
Answer: B
Question: Calculate 56581 ÷ ? = 137
A.113
B.213
C.413
D.417
Answer: C.413
Explanation: Answer
Let 56581/X = 137
Then X = 56581/137= 413
Option: C
Question: The average earning of a mechanic for the first-four days of a week is Rs. 16 and for the last four days is Rs. 24. If he earns Rs . 27 on the fourth day, his average earning for the whole week is ?
A.Rs . 18.95
B.Rs 16
C.Rs. 19
D.Rs. 25.71
Answer: C.Rs. 19
Explanation: Answer
Total earning for the week = Sum of earning of first four days + Sum of earning of last four days - Earning of 4th day
= 4 x16 + 4 x 24 -27
= Rs. 133
âˆ´ Average earning = 133 / 7
= Rs. 19
Correct Option: C
Question: A can do a piece of work in 3 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
A.12
B.9
C.8
D.6
Answer: D.6
Explanation: A's 1 hour's work = 1/3;
(B + C)'s 1 hour's work = 1/3 ;
(A + C)'s 1 hour's work = 1/2 .
(A + B + C)'s 1 hour's work = ( 1/3 + 1/3 ) =2/3 .
B's 1 hour's work = ( 2/3 - 1/2 ) = 1/6.
Therefore A alone will take 6 hours to do the work.
D
Question: Ten cards numbered 1 to 10 are placed in a box, mixed up thoroughly and then one card is drawn
randomly. If it is known that the number on the drawn card is more than 3, what is the probability
that it is an even number?
A.4/7
B.1/2
C.1/3
D.1/7
Answer: A.4/7
Explanation: Let A be the event ‘the number on the card drawn is even’ and B be the
event ‘the number on the card drawn is greater than 3’. We have to find P(A|B).
Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Then A = {2, 4, 6, 8, 10}, B = {4, 5, 6, 7, 8, 9, 10}
and A n B = {4, 6, 8, 10}
Also P(A) = 5/2, P(B) = 7/10 and P(A n B) = 4/10
Then P(A|B) = P(A n B)/P(B) = (4/10)/(7/10) = 4/7
A
Question: A pair of prime numbers that can be expressed in the form W{p, (p + 6)} is deﬁned as a pair of “sexy primes.” A “sexy triplet” is a group of three primes that can be expressed in the form {p, (p + 6), (p + 12)}. All of the following prime numbers are the middle term of a sexy triplet EXCEPT
A. 11
B. 13
C. 17
D. 19
Answer: D. 19
Explanation: definetly a sitter.plug in the values for middle term and calculate.We can see clearly that W for 19 , 19+6 gives 25 which is not a prime
therefore correct answer D
Question: If the radius of a circle is decreased 30%, what happens to the area?
A.51% decrease
B.20% decrease
C.36% decrease
D.40% decrease
Answer: A.51% decrease
Explanation: Area of Square = Pi* radius^2
New Radius = 0.7 * old radius
so new area = (0.7)^2 old area => 0.49 of old area => 49% old area
Ans : A
Question: Lucy is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of wheat, 3 morsels of rye, and 1 morsel of white. The pattern repeats after she leaves the morsel of rye. If Lucy drops 2,000 morsels of bread, what are the last 3 morsels of bread that she drops?
A.white − wheat − wheat
B.wheat − wheat − rye
C.rye − white− wheat
D.rye − rye − rye
Answer: A.white − wheat − wheat
Explanation: In a single round Lucy drops 6 morsels.
Remainder (2000/6) = 2
Final action = 2 drops of Wheat --> Options B, C, D and E can be eliminated
Answer: A
Question: The angles of a triangle have ratios 3:4:5 relative to each other. Determine which angle below corresponds to one of the angles of this triangle.
A.40Â°
B.60Â°
C.80Â°
D.100Â°
Answer: B.60Â°
Explanation: The three angles of a triangle add up to 180Â°. Knowing the ratios, we can formulate this expression:
3x + 4x + 5x = 180Â°
12x = 180Â°
x = 15Â°
Now, find the angles within the triangle.
3x = 3(15Â°) = 45Â°
4x = 4(15Â°) = 60Â°
5x = 5(15Â°) = 75Â°
Therefore, the answer is 60Â°, or B.
Question: What is the sum of the greatest common factor and the lowest common multiple of 16 and 72?
A.142
B.152
C.124
D.160
Answer: B.152
Explanation: Prime factorization of 16 = 2 x 2 x 2 x 2.
Prime factorization of 72 = 2 x 2 x 2 x 3 x 3
GCF = 8
LCM = 144
Sum = 152.
Answer B.
Question: Fred and Sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 2 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet?
A.5
B.9
C.25
D.30
Answer: C.25
Explanation: relative distance =35 miles
relative speed =2+5 =7 miles per hour
time taken =35/7=5 hours
distance travelled by sam =5*5=25 miles=C
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 5% from the list price. It may be sold at a profit of 25% on the cost price?
A.62.5
B.62.8
C.62.1
D.62.9
Answer: A.62.5
Explanation: Explanation:
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(95/100) = 59.375
MP = 62.5
Answer: A
Question: In how many ways, a committee of 6 members can be selected from 7 men and 4 ladies, consisting of 4 men and 2 ladies?
A.210
B.180
C.200
D.310
Answer: A.210
Explanation: (4 men out 7) and (2 ladies out of 4) are to be chosen
Required number of ways = 7C4*4C2 = 210
Answer is A
Question: A Table is bought for Rs.1600/- and sold at a loss of 20% find its selling price?
A.s.1280/-
B.s.1560/-
C.s.1580/-
D.s.1250/-
Answer: A.s.1280/-
Explanation: 100 % ------> 1600 (100 * 16 = 1600)
80 % ------> 1280 (80 * 16 = 1280)
Selling price = Rs.1280/-
Option 'A'
Question: What sum of money put at C.I amounts in 2 years to Rs.8820 and in 3 years to Rs.9261?
A.Rs.8000
B.Rs.8400
C.Rs.7500
D.Rs.7800
Answer: A.Rs.8000
Explanation: Explanation:
8820 ---- 441
100 ---- ? => 5%
x *105/100 * 105/100 = 8820
x*1.1025=8820
x=8820/1.1025 => 8000
Answer is A
Question: The ratio of two numbers is 2:3 and the sum of their cubes is 945. The difference of number is?
A.3
B.4
C.5
D.6
Answer: A.3
Explanation: 2x 3x
8x cube + 27x cube = 945
35x cube = 945
x cube = 27 => x = 3.Answer: A
Question: The diagonal of a rectangle is 41 cm and its area is 20 sq. cm. The perimeter of the rectangle must be:
A.18 cm
B.28 cm
C.30 cm
D.38 cm
Answer: A.18 cm
Explanation: l2 + b2 = 41.
Also, lb = 20.
(l + b)2 = (l2 + b2) + 2lb = 41 + 40 = 81
(l + b) = 9.
Perimeter = 2(l + b) = 18 cm.
A)
Question: At the starting of 2012, 60% of the population of Town Y lived in the north and the rest lived in the south. During the year 2012, the population of Town Y grew by 5.5%. If the population in the north grew by 4.5%, by how much did the population in the south grow?
A.7%
B.9%
C.1%
D.1.5%
Answer: A.7%
Explanation: Here I prefer the weighted average method over dealing with creating and solving the algebraic expression:
Ratio of population in the Town Y -North:South :: 60%:40% = 3:2
Mean growth = 5.5%
South Growth: 4.5%
North Growth = ??
North-------------Average--------------South
4.5% __(2n)_____5.5%_____(3n)_____??
Since:
4.5 + 2n = 5.5
n = 1/2 (this is the multiplier of the ratio)
Therefore:
South = 5.5 + 3n
South = 5.5 + 3(0.5) = 7%
Question: Three 6 faced dice are thrown together. The probability that all the three show the same number on them is?
A.1/39
B.1/36
C.1/32
D.1/31
Answer: B.1/36
Explanation: Explanation:
It all 3 numbers have to be same basically we want triplets. 111, 222, 333, 444, 555 and 666. Those are six in number. Further the three dice can fall in 6 * 6 * 6 = 216 ways.
Hence the probability is 6/216 = 1/36
Answer: B
Question: A started a business with Rs.25000 and is joined afterwards by B with Rs.30,000. After how many months did B join, if profit per annum is divieded equally?
A.2 months
B.4 months
C.5 months
D.7 months
Answer: A.2 months
Explanation: Given their profits are equal per annum so
25000*12=30000*x
x=10 months
12-10=2 months
ANSWER:A
Question: If k is a non-negative integer and 15^k is a divisor of 759,325 then 3^k - k^3 =
A.0
B.1
C.37
D.118
Answer: B.1
Explanation: At first we should understand whether 759325 divisible by 15.
15 is equal to 3 * 5 so 759325 should be divisible on these integers
759325 is divisible by 5 because of last digit 5
but not divisible by 3 because sum of its digits doesn't divisible by 3: 7 + 5 + 9 + 3 + 2 + 5 = 31 and 31 doesn't divisible by 3
so 759325 can be divisible by 15^k only if k = 0 and 15^k = 1
so 3^k - k^3 = 1 - 0 = 1
Answer is B
Question: J and M were each paid x dollars in advance to do a certain job together. J worked on the job for 12 hours and M worked for 2 hours less than J. If M gave J y dollars of her payment so that they would have received the same hourly wage, what was the dollar amount, in terms of y, that J was paid in advance?
A.a)4y
B.b)5y
C.c)6y
D.d)11y
Answer: D.d)11y
Explanation: J and M were both paid x dollars
If M gave Y dollars from her X to J then at the end
J will have X+Y dollars
M will have X- Y dollars
Now since the hourly wages have to be same then
Hourly wage of J = (X+Y) / 12 (Since J worked for 12 hrs)
Hourly wage of M = (X-y) /10 (Since M worked 2 hrs less than J)
Equating both
(X+Y)/12=(X-Y)/10
on simplifying X=11y
Answer D
Question: A bowl contains pecans, cashews, and almonds in a ratio of 7 : 12 : 18, respectively. If some of the nuts of one of the three types are removed, which of the following could be the ratio of pecans to cashews to almonds remaining in the bowl? i. 1 : 2 : 3 ii. 2 : 3 : 4 iii. 4 : 7 : 10
A.I only
B.III only
C.I,II only
D.II only
Answer: A.I only
Explanation: i. The ratio 2 : 3 is the same as the given ratio 12 : 18. If one pecan were removed, the new ratio would be 6 : 12 : 18, or 1 : 2 : 3.
ii. None of the nuts currently have a ratio of 3 : 4. The cashews and almonds do have a ratio of 2 : 3, but there are not enough pecans in the bowl to complete the ratio.
iii. The ratio 4 : 10 is the same as the given ratio 6 : 15. To see this, multiply the ratio by 3/2 . The new ratio is 6 : 10.5 : 15. Unfortunately, this means that there are fewer cashews that this ratio would require. Removing cashews won’t create the desired ratio.
Answer : A
Question: Four milkmen rented a pasture. A grazed 24 cows for 3 months; B 10 for 5 months; C 35 cows for 4 months and D 21 cows for 3 months. If A's share of rent is Rs. 2160, find the total rent of the field.
A.3750
B.3550
C.4250
D.9750
Answer: D.9750
Explanation: Ratio of shares of A, B, C, D = (24 x 3) : (10 x 5) : (35 x 4) : (21 x 3) = 72 : 50 : 140 : 63.
Let total rent be Rs. x. Then, A’s share = Rs. (72x)/325
(72x)/325=2160 = x=(2160 x 325)/72 = 9750
Hence, total rent of the field is Rs. 9750.
Answer is D.
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is ?
A.45 kmph
B.25 kmph
C.30 kmph
D.50 kmph
Answer: D.50 kmph
Explanation: Explanation:
Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec.
[(25/2) x (18/5)] km/hr = 45 km/hr.
Let the speed of the train be 'S' km/hr.
Then, relative speed = (S - 5) km/hr.
S - 5 = 45 => S = 50 km/hr.
ANSWER IS D
Question: Sreedhar and Sravan together can do a work in 25 days. With the help of Pavan, they completed the work in 8 days and earned Rs. 225. What is the share of Sravan, if Sreedhar alone can do the work in 75 days?
A.22
B.26
C.48
D.77
Answer: C.48
Explanation: Sravan's one day's work = 1/25 - 1/75 = 2/75
Sravan worked for 8 days. So, his 8 days work = 8 * 2/75 = 16/75
Sravan completed 16/75th of total work.
So, his share is 16/75 * 225 = Rs. 48.
Answer:C
Question: An examiner rejects 0.16% of the meters as defective. How many will be examine to reject 4?
A.500
B.4000
C.2500
D.5500
Answer: C.2500
Explanation: Explanation :
Solution: let the number of meters to be examined be x. then, 0.16% of x = 4
=>(16/100 * 1/100 * x) = 4
=>x = (4*100*100)/16 = 2500.
Answer : C
Question: An object thrown directly upward is at a height of h feet after t seconds, where h = -14 (t-3)^2 + 150. At what height, in feet, is the object 2 seconds after it reaches its maximum height?
A.80
B.88
C.94
D.112
Answer: C.94
Explanation: We see that h will be a maximum h=150 when t-3=0, that is when t=3.
At t=5, h = -14(5-3)^2 + 150 = -14(4) + 150 = 94
The answer is C.
Question: In a forest 150 deer were caught, tagged with electronic markers, then released. A week later, 50 deer were captured in the same forest. Of these 50 deer, it was found that 10 had been tagged with the electronic markers. If the percentage of tagged deer in the second sample approximates the percentage of tagged deer in the forest, and if no deer had either left or entered the forest over the preceding week, what is the approximate number of deer in the forest?
A.150
B.750
C.3,000
D.1,500
Answer: C.3,000
Explanation: The percentage of tagged deer in the second sample = 10/50*100=20%.
So, 150 tagged deers comprise 10% of total # of deers --> total # of deers = 150*20 = 3,500.
Answer: C
Question: There are 15 points in a given plane, no three of which are on the same line. If one of the points is represented as 'Y', then how many triangles can be determined with the 15 points that contain the point Y?
A.91
B.105
C.182
D.210
Answer: C.182
Explanation: Fist point is A which is fixed so can be selected in 1 way
Second point can be selected in 14 ways
Third point can be selected in 13 ways
so total ways = 1x14x13 = 182
but answer is 91 which is 182/2=C
Question: if 70% of (x-y) = 30% of (x+y) then what percent of x is y?
A.2.5%
B.40%
C.5%
D.15%
Answer: B.40%
Explanation: 70% of (x-y)=30% of(x+y)
(70/100)(x-y)=(30/100)(x+y)
7(x-y)=3(x+y)
4x=10y
x=5/2y
therefore required percentage
=((y/x) X 100)% = ((y/(5/2)y) X 100) =40%
Answer is B.
Question: A and B can do a work in 8 hours and 12 hours respectively. A starts the work at 6AM and they work alternately for one hour each. When will the work be completed?
A.9.6 days
B.7.6 days
C.4 days
D.8.6 days
Answer: A.9.6 days
Explanation: Work done by A and B in the first two hours, working alternately = First hour A + Second hour B = 1/8+ 1/12 = 5/24.
Total time required to complete the work = 2 * 24/5 = 9.6 days.
ANSWER:A
Question: If KING is coded as 17 and DON is coded as 18 Then MASS is coded as
A.21
B.20
C.19
D.29
Answer: D.29
Explanation: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DON = 4+14+15=33 i.e(3*3)+(3*3)=18
ANSWER:D
Question: Judges will select 5 finalists from the 7 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
A.10
B.21
C.210
D.420
Answer: C.210
Explanation: First Select 5 from 7 contestants and then select top 3 from those 5 =
7C5*5C3 = 42 * 5 = 210
ANS:C
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 40% marks is
A.5
B.4
C.3
D.2
Answer: A.5
Explanation: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.
The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.
Total ratio = 40
For 6 : (300/40)*6 = 45
Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.
Hence , there are 4 subject where he secured more that 40 %.
The answer is 5.
A
Question: 24 oz of juice P and 25 oz of juice V are mixed to make smothies A and Y . The ratio of p to V in smothie A is 4 is to 1 and that in Y is 1is to 5.How many ounces of juice P are contained in the smothie A?
A.5
B.10
C.15
D.20
Answer: D.20
Explanation: The ratio of p to V in smothie X is 4 is to 1 and that in Y is 1is to 5. p1 + p2 = 24
v1 + v2 = 25
p1 = 4v1
p2 = v2/5
4v1 + v2/5 = 24
v1 + v2 = 25
4v2 - v2/5 = 76
19v2/5 = 76 => v2 = 20
=> v1 = 5
=> p1 = 20
Answer - D
Question: Lucy bought a 1-year,10000 certificate of deposit that paid interest at an annual rate of 8 percent compunded semiannually. What was the total amount of interest paid on this certificate at maturity ?
A.10464
B.864
C.816
D.800
Answer: D.800
Explanation: Solution:
It says, 8 percent per annum per compounded semi annually.
Therefore r = 8/2 = 4% .
So, P = 10000
r = 4
n = 2
Net Amount A = 10816, I = 800.
ANSWER:D
Question: A shop owner sells 30mtr of cloth and gains SP of 10 mtrs. Find the gain %?
A.30%
B.40%
C.50%
D.60%
Answer: C.50%
Explanation: Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) – (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. Rs. 3000
Profit% = 10 × 100 = 50%
20
Profit of 50% was made by the merchant.
C
Question: In an election between two candidates, 75% of the voters cast thierthier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
A.1600
B.16000
C.16800
D.1680
Answer: C.16800
Explanation: Let the number of votes enrolled be x. Then ,
Number of votes cast =75% of x. Valid votes = 98% of (75% of x).
75% of (98% of (75%of x)) =9261.
[(75/100)*(98/100)*(75/100)*x] =9261.
X = [(9261*100*100*100)/(75*98*75)] =16800.
ANSWER C 16800
Question: KODAK bank offers an interest of 5% per annum compounded annually on all its deposits. If $10,000 is deposited, what will be the ratio of the interest earned in the 4th year to the interest earned in the 5th year?
A.1:5
B.625:3125
C.100:105
D.100^4:105^4
Answer: C.100:105
Explanation: Hi Bunuel,
Here is my approach: is this correct?
KODAK bank offers an interest of 5% per annum compounded annually on all its deposits.
Interest earned in 4 year= 10000(1+0.05)^4
Interest earned in 5 year= 10000(1+0.05)^5
Ratio= {10000(1.05)^4}/{10000(1.05^5)} =>1.05^4/1.05^5 =>1/1.05 Multiplied by 100 in both numerator and denominator gives 100:105
Hence Ans:C
Question: Virat buys an old car for Rs. 60000 and spends Rs. 4000 on its repairs. If he sells the scooter for Rs. 65000, his gain percent is:
A.3 (4/7) %
B.11 (1/9) %
C.12 (2/3) %
D.1.6%
Answer: D.1.6%
Explanation: Explanation:
C.P. = Rs. (60000 + 4000) = Rs. 64000
S.P. = Rs. 65000.
Gain% = ( (1000 / 64000) * 100 ) % = 1.6%
ANSWER D
Question: A solution of 90 litres contains milk and water in the ratio 7:x. If ten litres of water is added to the solution, the ratio becomes 3:2, find the value of x?
A.2
B.1.5
C.3.5
D.2.5
Answer: C.3.5
Explanation: Exp. Total new quantity = original sol + water =90+10 =100
New ratio = 3:2, New quantity of milk =3/5*100 = 60 Lit,
New quantity of water = 2/5*100= 40 Lit
Water present initially = (40-10) = 30 Lit
Ratio = 60/30 =7/x There for x = 3.5
Answer: C
Question: A man in a train notices that he can count 41 telephone posts in one minute. If they are known to be 50 metres apart, then at what speed is the train travelling?
A.620 km/hr
B.220 km/hr
C.220 km/hr
D.120 km/hr
Answer: D.120 km/hr
Explanation: Explanation:
Number of gaps between 41 poles = 40
So total distance between 41 poles = 40*50
= 2000 meter = 2 km
In 1 minute train is moving 2 km/minute.
Speed in hour = 2*60 = 120 km/hour
Answer: D
Question: An investor deposited $10,000 to open a new savings account that earned 8 percent annual interest, compounded quarterly. If there were no other transactions in the account, what was the amount of money in the account 6 months after the account was opened?
A.$10,200
B.$10,202
C.$10,400
D.$10,404
Answer: D.$10,404
Explanation: The amount in the account after 6 months is 1.02*1.02($10,000) = $10,404.
The answer is D.
Question: Find the odd man out. 30, -5, -45, -90, -145, -195, -255
A.-145
B.-195
C.-30
D.-90
Answer: A.-145
Explanation: 30
30 - 35 = -5
-5 - 40 = -45
-45 - 45 = -90
-90 - 50 = -140
-140 - 55 = -195
-195 - 60 = -255
Hence, -145 is wrong. -140 should have come in place of -145
Answer is A
Question: How many positive integers less than 8,000 are there in which the sum of the digits equals 5?
A.57
B.56
C.55
D.54
Answer: B.56
Explanation: Basically, the question asks how many 4 digit numbers (including those in the form 0XXX, 00XX, and 000X) have digits which add up to 5. Think about the question this way: we know that there is a total of 5 to be spread among the 4 digits, we just have to determine the number of ways it can be spread.
Let X represent a sum of 1, and | represent a seperator between two digits. As a result, we will have 5 X's (digits add up to the 5), and 3 |'s (3 digit seperators).
So, for example:
XX|X|X|X = 2111
||XXX|XX = 0032
etc.
There are 8C3 ways to determine where to place the separators. Hence, the answer is 8C3 = 56.
B
Question: If 204 ÷ 12.75 = 16, then 2.04 ÷ 1.275 = ?
A.16
B.1.6
C.0.16
D.0.016
Answer: B.1.6
Explanation: Explanation :
(204/12.75) = 16
⇒ (20.4)/(1.275) = 16 (∵ Divided Numerator and Denominator by 10)
⇒ 2.04/1.275 = 1.6 (∵ Divided LHS and RHS by 10) Answer : Option B
Question: In a deck of cards there are 50 cards numbered from 1 to 13. There are 4 cards of each number in the deck. If you insert 12 more cards with the number 10 on them and you shuffle the deck really good, what is the probability to pull out a card with a number 10 on it?
A.1/4.
B.4/17.
C.5/29.
D.8/31.
Answer: D.8/31.
Explanation: 4+12 tens/50+12 total cards=16/62=8/31
D
Question: If x is a whole number, then x²(x² - 1) is always divisible by
A.12-x
B.Multiple of 12
C.12
D.24
Answer: C.12
Explanation: Putting x = 2,we get 2²(2² - 1) = 12.
checking with other integers, the above equation always gives a value which is a multiple of 12,
So, x²(x² - 1) is always divisible by 12.
ANSWER:C
Question: AB
+BA
___
121
In the addition problem above, A and B represent digits in two different two-digit numbers. What is the sum of A and B?
A.6
B.8
C.9
D.11
Answer: D.11
Explanation: two ways to do it..
1) straight logic..
we can see that ones digit is 1 when units digit B and A are added..
answer has to be 1 in the units digit..
only 11 fits in..
2) BA=10B+A, and
AB=10A+B..
it is given that BA+AB=121..
or 10B+A +10A+B=121..
11(A+B)=121..
so A+B=11..
ANSWER:D
Question: Calculate the average mark scored by Adam if he had the following scores in an examination: 86, 75, 72, 63 and 65 marks (out of 100) in French Language, Geography, Art and design, History and Physical Education respectively?
A.39.2
B.79.2
C.72.2
D.71.2
Answer: C.72.2
Explanation: Explanation:
Average mark = 86+75+72+63+65/5=72.2
Answer: Option C