divelab/Sys2Bench huggingface dataset:
Question: An engineer designed a ball so that when it was dropped, it rose with each bounce exactly one-half as high as it had fallen. The engineer dropped the ball from a 10-meter platform and caught it after it had traveled 29.65 meters. How many times did the ball bounce?
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: Ans: 6
Division of total diatance travelled will be 10+10+5+2.5+1.25+0.6+0.3 ANS B
Answer: B
Question: If the units digit of n^43 is 7, which of the following could be the value of n?
I. n = 41
II. n = 43
III. n = 47
Options:
A)Only I
B)Only II
C)Only III
D)I and II
E)II and III
Rationale: I tried in this way.
Given n^43 units digit is 7.
If at all we have to get 7 as units digits only 3 and 7 series has 7
3^! = 3 , 3^2 = 9 , 3^3 = 27 , 3^4 = 81
7^1 = 7, 7^2 = 49 , 7^3 = 3 (units ) , 7^4 = 1 (units)
We have n^43 - then divide 43 by 4 = reminder 3.
Then we have for only 7^3 - we have units digit as 7.
Hence 47^43 = 7 (units).
Option A is correct answer , and with 41^43 we always get 1 as units digit and 43^43 - we get units as 3.
Answer: A
Question: What is the units digit of the product of the first 50 odd numbers?
Options:
A)0
B)1
C)2
D)3
E)5
Rationale: 1*3*5*7 ................... will end up in 5 in the units place
Answer : E
Answer: E
Question: The sale price of a trolley bag including the sale tax is Rs. 1190. The rate of sale tax is 12% . If the shopkeeper has made a profit of 25%, the cost price of the trolley bag is:
Options:
A)Rs 800
B)Rs 820
C)Rs 860
D)Rs 850
E)None of these
Rationale: Explanation :
112% of S.P. = 1190
S.P. = Rs.(1190 x 100/112) = Rs.1062.50.
C.P. = Rs (100/125x 1062.50) = Rs 850
Answer : D
Answer: D
Question: On his first 3 tests, Rajeev received an average score of N points. If on his fourth test, he exceeds his previous average score by 20 points, what is his average score for his first 4 tests?
Options:
A)N
B)N + 4
C)N + 5
D)N + 10
E)N + 20
Rationale: Total points from first three tests: 3N
Points on fourth test: N + 20
Total points on all four tests: 3N + (N + 20) = 4N + 20
Average score for first four tests: (4N + 20)/4 = N + 5
Answer is C.
Answer: C
Question: which number need to add to 859622 to get a number exactly divisible by 456?
Options:
A)547879
B)354643
C)354673
D)575673
E)859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: E
Question: The triangle ABC has sides of the following lengths: AB = 24, BC = 7, and AC = 25.
Let M be the midpoint of AB. What is the length of CM?
Options:
A)1
B)root139
C)12
D)root193
E)16
Rationale: Since 242 + 72 = 252, triangle ABC is a right triangle. Thus, MBC is also a right
triangle and CM2 = BM2 + BC2 = 122 + 72 = 193.
correct answer D
Answer: D
Question: Due to flooding, vendors increased the cost of sandbags by 30% to keep customers from buying out all the sandbags. Government officials declared an emergency and would only pay 60% of total price for sandbags. What is the difference between the new cost of the sandbags and the amount government officials paid?
Options:
A)12.0%
B)15.0%
C)20.0%
D)22.0%
E)25.0%
Rationale: Quantity X Rate = Price
1 X 1 = 1
0.60 X 1.30 = 0.780
Decrease in price = (0.22/1) Ã— 100 = 22.0%
Answer = Option D
Answer: D
Question: The 7th grade French and Spanish classes each have 21 students in them, and there are six students in the 7th grade taking both languages. If everyone in the 7th grade is in at least one of the two language classes, how many students are taking just one of the two classes?
Options:
A)24
B)28
C)30
D)32
E)34
Rationale: French class + Spanish class = 42 students.
Six students are in both classes so they were counted twice.
The number of students taking just one class is 42 - 2(6) = 30.
The answer is C.
Answer: C
Question: 2+2+2²+2³ ... +2^6
Options:
A)2^9
B)2^10
C)2^16
D)2^35
E)2^7
Rationale: 2+2=2^2
2^2+2^2=(2^2)*(1+1)=2^3
2^3+2^3=(2^3)*(1+1)=2^4
Answer E
Answer: E
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
Options:
A)175/256
B)451/365
C)312/456
D)156/754
E)164/784
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans:A
Answer: A
Question: x, a, z, and b are single digit positive integers. x = 1/3a. z = ¼3b. (10a + b) – (10x + z) could NOT equal
Options:
A)31
B)32
C)46
D)64
E)68
Rationale: a=3x , b =3z therefore(3x.10+3z) - (10x +z) = (3-1) (10x+z) =2.(10x+Z)
number should be divisible by 2
A
Answer: A
Question: The area of a triangle is 615 m2. If one of its sides is 123 metre, find the length of the perpendicular dropped on that side from opposite vertex.
Options:
A)15 metres
B)12 metres
C)10 metres
D)9 metres
E)None of these
Rationale: In a triangle,
Area = 1⁄2 × length of perpendicular × base
or 615 = 1⁄2 × length of perpendicular × 123
∴ Length of perpendicular = 615×2/123=10m
Answer C
Answer: C
Question: If the cost price of 50 articles is equal to the selling price of 20 articles, then the gain or loss percent is?
Options:
A)16
B)127
C)12
D)18
E)150
Rationale: Percentage of profit = 30/20 * 100 = 150%
Answer: E
Answer: E
Question: 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
Options:
A)4
B)7
C)9
D)14
E)None
Rationale: 1 woman's 1 day's work = 1/70
1 Child's 1 day's work = 1/140
5 Women and 10 children 1 day work = (5/70+10/140)=1/7
So 5 women and 10 children will finish the work in 7 days.
Answer: B
Answer: B
Question: What is the remainder when 1014*1047*1050*1053 is divided by 33?
Options:
A)3
B)6
C)30
D)21
E)18
Rationale: OA is 'C'.
OE:
take the remainder from each of 1044/33, 1047/33 and so on..
1014/33 gives remainder = 24
1047/33 gives remainder = 24
1050/33 gives remainder = 27
1053/33 gives remainder = 30
the net remainder is the product of above individual remainders. i.e = 24*24*27*30
break them into pairs 24*24/33 gives remainder 15
and 27*30/33 gives remainder 18
so 15*18/33 gives remainder 6.
B
Answer: B
Question: Alice and Bob will throw three dice each. The score is the sum of points on all three dice. If Alice scores 17 in her attempt what is the probability that Bob will outscore Alice in his attempt?
Options:
A)1/216
B)5/216
C)7/216
D)1/36
E)5/36
Rationale: The total number of ways the dice can land is 6*6*6=216.
Bob must get a score of 18=6+6+6.
There is only 1 way to do this.
P(Bob wins)=1/216
The answer is A.
Answer: A
Question: Nine family members: 5 grandchildren (3 brothers and 2 sisters) and their 4 grandparents are to be seated around a circular table. How many different seating arrangements are possible so that 2 sisters are seated between any two of the three brothers?
Options:
A)120
B)480
C)1440
D)2880
E)8640
Rationale: Consider two brothers and two sisters between them as one unit: {BSSB}.
So, now we have 6 units: {G}, {G}, {G}, {G}, {B}, and {BSSB}.
These 6 units can be arranged around a circular table in (6-1)!=5! ways.
Next, analyze {BSSB} unit:
We can choose 2 brothers out of 3 for the unit in C23=3C32=3 ways;
These brothers, within the unit, can be arranged in 2! ways: {B1,S,S,B2}{B1,S,S,B2} or {B2,S,S,B1}{B2,S,S,B1}
The sisters, within the unit, also can be arranged in 2! ways: {B,S1,S2,B}{B,S1,S2,B} or {B,S2,S1,B}{B,S2,S1,B}
Therefore, the final answer is 5!*3*2*2=1440.
Answer: C.
Answer: C
Question: When Jessica withdrew $200 from her bank account, her account balance decreased by 2/5. If she deposits an amount equal to 2/3 of the remaining balance, what will be the final balance in her bank account?
Options:
A)300
B)375
C)400
D)500
E)575
Rationale: As per the question 200=2a/5
thus- a which is the total amount =500
The amount thus left =300
She then deposited 2/3 of 300=200
total amount in her account =500
Answer D
Answer: D
Question: By selling 150 mangoes, a fruit-seller gains the selling price of 30 mangoes. Find the gain percent?
Options:
A)11
B)25
C)7
D)88
E)98
Rationale: SP = CP + g
150 SP = 150 CP + 30 SP
120 SP = 150 CP
120 --- 30 CP
100 --- ? => 25%
Answer: B
Answer: B
Question: The mean of 50 observations is 200. But later he found that there is decrements of 9 from each observations. what is the the updated mean is ?
Options:
A)165
B)185
C)190
D)191
E)199
Rationale: 191
Answer is D
Answer: D
Question: A man rows his boat 78 km downstream and 50 km upstream, taking 2 hours each time. Find the speed of the stream?
Options:
A)76 kmph
B)6 kmph
C)14 kmph
D)7 kmph
E)4 kmph
Rationale: Speed downstream = d/t = 78/(2)
= 39 kmph
Speed upstream = d/t = 50/(2)
= 25 kmph
The speed of the stream = (39 - 25)/2
= 7 kmph
Answer:D
Answer: D
Question: The food in a camp lasts for 34 men for 56 days. If fourteen more men join, how many days will the food last?
Options:
A)80 days
B)30 days
C)65 days
D)40 days
E)42 days
Rationale: one man can consume the same food in 34*56 = 1904 days.
14 more men join, the total number of men = 48
The number of days the food will last = 1904/48
= 40 days.
Answer:D
Answer: D
Question: An amount of money is to be distributed among Faruk, Vasim and Ranjith in the ratio 3 : 5 : 11. If Vasims share is Rs. 1500, what is the difference between Faruk's and Ranjith's shares?
Options:
A)s 1200
B)s 1500
C)s 1600
D)s 1900
E)s 2400
Rationale: Explanation :
Let P = Faruk, Q = Vasim, R = Ranjith
Let P = 3x, Q = 5x and R = 11x.
Then, 5x = 1500 ? x = 300. P=900,Q=1500 and R = 3300.
Hence, (R - p) = (3300 - 900) = 2400
Answer : E
Answer: E
Question: What is the CP of Rs 100 stock at 8 discount, with 1/5% brokerage?
Options:
A)92.9
B)96.3
C)92.2
D)96.7
E)92.8
Rationale: Explanation:
Use the formula,
CP= 100 â€“ discount + brokerage%
CP= 100-8+1/5
92.2
Thus the CP is Rs 92.2.
ANSWER: C
Answer: C
Question: Take number 1000 and then add 20 to it.
Now add 1000 one more time.
Now add 30.
Now add 1000 one more time.
Now add 40.
Now add 1000 one more time.
Now add 10.
What is the total?
Options:
A)4100
B)3870
C)5200
D)6230
E)8340
Rationale: A
4100
some people might guess 5000
Answer: A
Question: The edges of three metal cubes are 2 cm, 3 cm, and 4 cm respectively. A new cube is made by melting these three cubes together. What is the edge of the new cube (in centimeters)?
Options:
A)4.0
B)4.2
C)4.4
D)4.6
E)4.8
Rationale: The total volume is 2^3+3^3+4^3=99
The edge of the new cube is the cube root of 99 which is about 4.6 cm.
The answer is D.
Answer: D
Question: Each shelf of a bookcase contains 22 books. If the librarian took out 40 books and rearranged the remaining books so that all shelves but the last one contained 16 books and the last shelf contained 18 books, how many shelves does the bookcase have?
Options:
A)A)4
B)B)5
C)C)7
D)D)8
E)E)9
Rationale: Denoting x the number of the shelves,
we can build an equation: 22x=16(x−1)+18+40
Solving the equation, we get x=7
Answer: C
Answer: C
Question: A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40
B)28
C)27
D)17
E)21
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25
= 40 sec
Answer: A
Answer: A
Question: In a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water be 6 km/hr, find the total journey time.
Options:
A)10 hours
B)12 hours
C)14 hours
D)15 hours
E)None of these
Rationale: Explanation :
speed of the boat = 6 km/hr
Speed downstream = (6+2) = 8 km/hr
Speed upstream = (6-2) = 4 km/hr
Distance travelled downstream = Distance travelled upstream = 40 km
Total time taken = Time taken downstream + Time taken upstream
= (40/8) + (40/4) = 15
D
Answer: D
Question: If (6)(x^2) has three different prime factors, at most how many different prime factors does x have?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: x can have at most 3 prime factors, namely the prime factors 2 and 3, plus one other.
If x had more than this number of prime factors, then (6)(x^2) would have more than 3 prime factors.
The answer is C.
Answer: C
Question: Five years ago Anita was P times as old as Ben was. If Anita is now 14 years old, how old is Ben now in terms of P ?
Options:
A)9/P + 5
B)P/9 +5
C)17 - P/5
D)17/P
E)11.5P
Rationale: let's call Ben age five years ago is x
so five years ago Anita was: 14-5 = 9 years old
and five years ago Anita was P times as old as Ben was
=> 9/x = P
=> x = 9/P
=> Now Ben age will be : x+5 = 9/P+5
=> the answer is A
Answer: A
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?
Options:
A)197
B)280
C)189
D)278
E)268
Rationale: x*(85/100)
= (480 - x)119/100
x = 280
Answer: B
Answer: B
Question: The salary of a person was reduced by 10%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
Options:
A)10%
B)11 1/9%
C)13 2/7%
D)15 3/11%
E)12 1/3%
Rationale: Let the original salary be $100
New salary = $90
Increase on 90 =10
Increase on 100 = 10/90 * 100 = 11 1/9%
Answer is B
Answer: B
Question: A person traveled from his house to office at 30 kmph; then he was late to his office by 5 minutes. If he increases his speed by 10 kmph he would be early by 15 minutes to his office. What should be his speed so that he reaches his office on time ?
Options:
A)36 kmph
B)32 kmph
C)34 kmph
D)35 kmph
E)36 kmph
Rationale: Expl :
Let the distance between house and office be x km
(x/30) – (x/40) = 20/40; x/120 = 1/3 x = 40 km
Travlling at 40 kmph, he reaches office in 1 hour i.e. 15 minutes early
So required speed = 40/ 5/4 = 40 * 4/5 = 160/5 = 32 kmph
Answer: B
Answer: B
Question: The average weight of 3 men A, B and C is 84 kg. Another man D joins the group and the average now becomes 80 kg. If another man E, whose weight is 3 kg more than that of D, replaces A, then average weight of B, C, D and E becomes 79 kg. The weight of A is?
Options:
A)70 kg
B)72 kg
C)75 kg
D)80 kg
E)None of these
Rationale: Weight of D = (80 x 4 - 84 x 3) kg = 68 kg
Weight of E = (68 + 3) kg = 71 kg
(B + C + D + E)’s weight = (79 x 4) kg = 316 kg
Therefore, (B + C)’s weight = [316 - (68 + 71)] kg = 177 kg.
Hence, A’s weight = [(84 x 3) - 177] kg = 75 kg.
ANSWER:C
Answer: C
Question: Set Y consists of the following unique integers: -2, 17, 3, n, 2, 15, -3, and -27; which of the following could be the median of set Y?
Options:
A)767
B)76
C)7
D)5
E)1
Rationale: Whenever a question asks you to deal with the MEDIAN of a group of numbers, you MUST put the numbers in order from least to greatest (or at the very least,group offthe numbers so that you can restrict the potential value of the median).
Here, we have 8 values (one of the values is the variable N). We're told that the values are UNIQUE, so N CANNOT be any of the other 7 values listed. We're asked which of the following answers COULD be the median, so if we determine that one of the answer choices is a POSSIBLE median, then we can stop working....
Since the group includes 8 values, the median will be the AVERAGE of the 4th and 5th values...
Putting the 7 numbers in order, we have:
-27, -3, -2, 2, 3, 15, 17
This means that the2will either be the 4th term or the 5th term (depending on the value of N).
IF....
N is REALLY BIG, then the 4th and 5th terms will be 2 and 3, so the median will = 2.5
N is REALLY SMALL, then the 4th and 5th terms will be -2 and 2, so the median will = 0
Neither of those answers is among the choices though, so N must be something relativelycloseto 2.....
IF....
N = 0, then the 4th and 5th terms will be 0 and 2, so the median will = 1. That answer IS among the choices, so we're done.
E
Answer: E
Question: The average amount with a group of seven numbers is Rs. 20. If the newly joined member has Rs. 50 with him, what was the average amount with the group before his joining the group?
Options:
A)Rs.13
B)Rs.12
C)Rs.15
D)Rs.22
E)Rs.12
Rationale: Total members in the group = 7
Average amount = Rs. 20
Total amount with them = 7 * 20 = Rs. 140
One number has Rs. 50. So, the amount with remaining 6 people = 140 - 50 = Rs. 90
The average amount with them = 90/6 = Rs.15.
Answer:C
Answer: C
Question: If x and y are prime numbers such that x > y > 3, then x^2 − y^2 must be divisible by which one of the following numbers?
Options:
A) 3
B) 4
C) 5
D) 9
E) 12
Rationale: If x=8 and y=6, then x^2-y^2=28 and 28 is divisible only by 4 from the options, thus it must be correct.
Answer: B.
Answer: B
Question: In each term of a sequence, 9 is added to get the next term. If the first term is 2, what is the eighty-first term?
Options:
A)632
B)695
C)713
D)722
E)731
Rationale: Let’s think about the first few terms of this sequence.
a_1=2
a_2=11 = 2 + 9
a_3=20 = 2 + 9 + 9
a_4=29 = 2 + 9 + 9 + 9
To find each new term, we add 9. The result is, each term equals 2 plus a sum of 9’s. How many nines? Well, the second term has one 9, the third term has two 9’s, the fourth term has three 9’s, so it’s clear the nth term would have a sum of (n – 1) 9’s. Thus, the eighty-first term would be 2 plus eighty 9’s. Well, eighty 9’s = 80*9 = 720, so the eighty-first term = 722, answer D.
Answer: D
Question: How many of the positive factors of 20 are not factors of 24
Options:
A)2
B)3
C)4
D)1
E)5
Rationale: factors of 20 - 1, 2, 4,5, 10, 20
factors of 24 -1, 2, 3, 4, 6, 8, 12 and 24
Comparing both, we have 3 factors of 20 which are not factors of 24- 5,10,20
Answer : B
Answer: B
Question: If 5 persons can do 5 times of a particular work in 5 days, then, 3 persons can do 3 times of that work in?
Options:
A)2 days
B)3 days
C)5 days
D)7 days
E)9 days
Rationale: That is, 1 person can do one time of the work in 5 days.
Therefore, 3 persons can do 3 times work in the same 5 days itself.
C)
Answer: C
Question: The profits of a firm are to be distributed in a suitable ratio. Suitable ratio is the ratio whose terms differ by 40 and the measure of which is 2/7. Find the suitable ratio.
Options:
A)280 : 2
B)16 : 56
C)80 : 7
D)40 : 14
E)none of these
Rationale: Let the ratio be x : y
Given x/y = 2/7,
Also y - x = 40,
Solving we get, x = 16, y = 56
ANSWER:B
Answer: B
Question: The probability that a girl student gets scholarship is 0.6 and that of a boy is 0.8,then probability that at least one gets the scholarship is:
Options:
A)0.72
B)0.82
C)0.92
D)1.12
E)1.22
Rationale: Probability that girl gets scholarship = 0.6
Probability that boy gets scholarship = 0.8
Hence, Probability that girl don't get scholarship = 1-0.6 = 0.4
Probability that boy don't get scholarship = 1-0.8 = 0.2
So, Probability that at least one gets scholarship is: (Girl gets and Boy don't get) OR (Boy gets and Girl don't get) OR (Both Gets)
=(0.6*0.2)+(0.8*0.4)+(0.6*0.8)
=0.12+0.32+0.48
=0.92
ANSWER:C
Answer: C
Question: 1.A committee that includes 6 members is about to be divided into 2 subcommittees with 3 members each. On what percent of the possible subcommittees that Michael is a member of is David also a member
Options:
A)A.10%
B)B.20%
C)C.45%
D)D.55%
E)E.50%
Rationale: A,B, C is too low so I eliminated those answers, E was too high of a number, so I chose D as my final answer.C
Answer: C
Question: An organisation has 3 committees, only 2 persons are members of all 3 committee but every pair of committee has 3 members in common. what is the least possible number of members on any one committee?
Options:
A)6
B)7
C)8
D)9
E)4
Rationale: Total 4 members minimum required to serve only on one committee.
\Answer:E
Answer: E
Question: What percent of a day is 6 hours?
Options:
A)6.25%
B)20%
C)25%
D)12.5%
E)10 %
Rationale: Total hours in a day = 24
Required percent =6×100=25%
---
24
Answer: Option C
Answer: C
Question: In how many ways a committee of 5 members can be selected from 6men and 5ladies, consisting of 3 men and 2 ladies?
Options:
A)120
B)115
C)250
D)160
E)200
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen
Required number of ways = 6C3 * 5C2 = (6*5*4*5*4)/(3*2*1*2*1) = 200
Answer is E
Answer: E
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?
Options:
A)4320
B)4325
C)4330
D)4884
E)4336
Rationale: Divisor = (5 * 44) = 220
= 10 * Quotient = Divisor
=> Quotient = 220/10 = 22
Dividend = (Divisor * Quotient) + Remainder
Dividend = (220 * 22) + 44 = 4884
D
Answer: D
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 18 hours and 8 hours respectively. The ratio of their speeds is
Options:
A)4 : 9
B)4 : 3
C)4 : 12
D)4 : 8
E)4 : 5
Rationale: Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 8 : 18 = 4 : 9.Answer: A
Answer: A
Question: Average of money that group of 4 friends pay for rent each month is $800.After one persons rent is increased by 25% the new mean is $850.What was original rent of friend whose rent is increased?
Options:
A)800
B)900
C)1000
D)1100
E)1200
Rationale: 0.25X = 4(850-800)
0.25X = 200
X = 800
answer A
Answer: A
Question: There are 14 stations between Hyderabad and Bangalore. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
Options:
A)288
B)267
C)261
D)211
E)240
Rationale: The total number of stations = 16
From 16 stations we have to choose any two stations and the direction of travel (i.e., Hyderabad to Bangalore is different from Bangalore to Hyderabad) in 16P₂ ways.
16P₂ = 16* 15= 240.
Answer: E
Answer: E
Question: If 2x + y = 26 and x + 2y = 10, then (x + y)/3 =
Options:
A) 1
B) 4/3
C) 17/5
D) 18/5
E) 4
Rationale: We have two equations:
2x + y = 26
x + 2y = 10
Notice that something nice happens when we ADD them. We get:
3x + 3y = 36
Divide both sides by 3 to get:x + y = 12
So, (x + y)/3 =12/3=4
Answer: E
Answer: E
Question: Two same glasses are respectively 1/4th 1/5th full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is?
Options:
A)9:37
B)9:31
C)9:38
D)9:32
E)9:35
Rationale: 1/4 : 3/4 = (1:3)5 = 5:15
1/5 : 4/5 = (1:4)4 = 4:16
------
9:31
Answer: B
Answer: B
Question: A sum of money becomes double itself in 8 years at simple interest. How many times will it become 12 years at the same rate?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: P ---- 2P ---- 8 years3P ---- 12 years Answer: C
Answer: C
Question: 18 men take 21 days of 8 hours each to do a piece of work. How many days of 6 hours each would 21 women take to do the same. If 3 women do as much work as 2 men?
Options:
A)32
B)87
C)36
D)99
E)77
Rationale: 3W = 2M
18M ------ 21 * 8 hours
21 W ------ x * 6 hours
14 M ------ x * 6
18 * 21 * 8 = 14 * x * 6
x = 36
Answer: C
Answer: C
Question: A utensil contain the amount of milk which is as much lesser than 80 is more than 42. The amount of milk is?
Options:
A)45
B)49
C)71
D)61
E)56
Rationale: Answer
Let the amount be x.
Then, x - 42= 80- x
’ 2x = 80+ 42= 122
2x = 122
´ x = 61
Correct Option: D
Answer: D
Question: If 16 men working 7 hours day can plough a fieid in 4l days, inhow many days will 14 men working 12 hours a clay plough the samefield ?
Options:
A)22
B)32
C)36
D)39
E)40
Rationale: Explanation :
(Men 14 : 16) : (Hrs/Day 12 : 7) :: 48 : x14 * 12 * x = 16 * 7 * 48 or x = 32
Answer : B
Answer: B
Question: The product of two positive integers is 783 and their difference is 2. What is the bigger number?
Options:
A)23
B)25
C)27
D)29
E)31
Rationale: Let's use trial and error to find the two numbers.
30*28 = 840 (too high)
29*27 = 783
The answer is D.
Answer: D