divelab/Sys2Bench huggingface dataset:
Question: At Atira's party there were five times as many females as males. There were three times as many adults as children. Which of the following could NOT be the number of people at the party?
Options:
A)384
B)258
C)216
D)120
E)72
Rationale: we have to work on the info and understand what that info takes us to...
1) there were five times as many females as males At Atira's party..
this means F=5M.. so total number=6M..
2) There were three times as many adults as children..
A=3C...
or total = 4C..
so the total is 4C or 6M..
since C and M have to be positive integers, we can say for sure that Total is a multiple of 4 and 6..
or Total is multiple of LCM of 4,6..
LCM of 4,6= 12..
lets see which number is not multiple of 12..
A. 384...12*32
B. 258... no
C. 216....12*18
D. 120....12*10
E. 72......12*6..
so B is our answer..
Answer: B
Question: A sum was put at simple interest at a certain rate for 4 years Had it been put at 2% higher rate, it would have fetched 56 more. Find the sum.
Options:
A)500
B)600
C)700
D)800
E)None of these
Rationale: Difference in S.I. = P×T/100(R1−R2)
⇒ 56 = P×4×2/100(∵ R1 - R2 = 2)
⇒ P = 56×100/4×2=700
Answer C
Answer: C
Question: The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.40 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost?
Options:
A)399
B)272
C)932.4
D)277
E)311
Rationale: Answer: Option C
Explanation:
a2 = 3136 => a = 56
56 * 4 * 3 = 672 â€“ 6 = 666 * 1.4 = 932.4 Answer: C
Answer: C
Question: In a urban village of india named "owlna" , 70% people have refrigerator , 75% people have television , 90% people got computers and 85% got Air-conditionor. how many people(minimum) got all these luxury.
Options:
A)23%
B)17%
C)11%
D)10%
E)20%
Rationale: E
10%
100 - [ (100-85)+(100-90)+(100-75) +(100-70)]
=100-(30+25+10+15)
=100-80
Answer: E
Question: A box contains 3 blue marbles, 4 red, 6 green marbles and 2 yellow marbles. If three marbles are drawn what is the probability that one is yellow and two are red?
Options:
A)12/459
B)12/489
C)12/455
D)12/454
E)12/451
Rationale: Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.
When three marbles are drawn, the probability that one is yellow and two are red
= (²C₁)(⁴C₂)/¹⁵C₃
= (2 * 4 * 3 * 3 * 2)/(1 * 2 * 15 * 14 * 13)
= 12/455
Answer: C
Answer: C
Question: A can do a piece of work in 18 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in
Options:
A)5days
B)6days
C)7.5days
D)8.5days
E)9days
Rationale: Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =18∗1/2=9 days
Option E
Answer: E
Question: There are y different travelers who each have a choice of vacationing at one of n different destinations. What is the probability that all y travelers will end up vacationing at the same destination?
Options:
A)1/n!
B)n/n!
C)1/n^y
D)1/n^(y-1)
E)n/y^n
Rationale: The simplest way to look at it is to assume that the first traveler picks a place. All the remaining travelers (given as y-1) now need to pick the same place for vacation.
As a result the probability is equivalent to (1/n) for each traveler to pick that same spot as the original traveler, which has to happen (y-1) times.
P=1n∗1n∗...∗1nP=1n∗1n∗...∗1n (y-1) times
P=1n(y−1)
The answer is D: 1/n^(y-1).
Answer: D
Question: 1/7 of 133 of 46% of 924 = ?
Options:
A)7075
B)8025
C)8075
D)9025
E)9075
Rationale: Explanation :
? = 1/7 x 133 x 46/100 x 924
= 8075.76 = 8075
Answer : Option C
Answer: C
Question: Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers?
Options:
A)8 hours and 24minutes.
B)6 hours and 45 minutes.
C)3 hours and 60 minutes.
D)4 hours and 30 minutes.
E)2 hours and 19 minutes.
Rationale: The time it takes Kim to walk 18 kilometers is equal to
18 / 4 = 4.5 hours = 4 hours + 0.5 ? 60 minutes
= 4 hours and 30 minutes.
correct answer D
Answer: D
Question: In a bag there are a certain number of blue balls and white balls. The probability of picking up exactly 1 white ball when 2 balls are randomly drawn, is 1/2. Which of the following is the ratio of the number of blue balls to white balls in the bag
Options:
A)1:1
B)1:2
C)1:5
D)1:4
E)1:6
Rationale: since the probability of drawing a white ball out of two picks is 1/2.
the ratio of the white ball to blue balls should be 1:1
Answer : A
Answer: A
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability T that the number of men is equal to that of women?
Options:
A)T=18/35
B)16/35
C)14/35
D)13/35
E)12/35
Rationale: METHOD- 1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Answer: A
Question: An investor receives a total combined return of 7% on his two different investments. On his $40,000 investment he receives a return of 6%. What is the return on his $20,000 investment?
Options:
A)7.25%
B)7.5%
C)8%
D)8.5%
E)9%
Rationale: 0.06 * 40000 + 20000x = 0.07(60000)
solving for x give x = 9%
option E
Answer: E
Question: It is the New Year and Mandy has made a resolution to lose weight this year. She plans to exercise and do yoga. For exercise she plans to workout at the gym and ride her bicycle in the ratio of 2:3 everyday. She will also do yoga in the ratio, yoga:exercise = 2:3. If she rides her bike for 16 minutes, how much time will she spend doing yoga? (rounded to minutes)
Options:
A)10 min.
B)41 min.
C)27 min.
D)23 min.
E)25 min.
Rationale: The ratio is 2:3 = gym:ride, so (16)(3/2) = 24 minutes at the gym, and 24 + 16 = 40 minutes exercise, so (2/3)(40) = 27 minutes yoga.
Answer: C
Answer: C
Question: The probability of two events A and B are0.25 and 0.40 respectively. The probability that both A and B occur is 0.20. The probability that neither A nor B occur is _________
Options:
A)0.45
B)0.4
C)0.55
D)0.05
E)0.6
Rationale: we are apply that formula..............
P(AorB)=P(A)+P(B)-P(A AND B)
=.25+.40-.20
=.45
but the probability of neither A nor B=1-.45
=0.55
ANSWER:C
Answer: C
Question: A jar contains only three types of objects: red, blue, and silver paper clips. The probability of selecting a red paper clip is 3/7, and the probability of selecting a blue paper clip is 1/7. What is the probability of selecting a silver paper clip?
Options:
A) 1/12
B) 1/2
C) 3/7
D) 3/4
E) 11/12
Rationale: Prob of Red = 3/7
Prob of Blue = 1/7
Prob of Silver = ?
P(Silver) = 1 - P(Red) - P(Blue) ==> 1-1/7-3/7 = 3/7
Ans: C
Answer: C
Question: The average of 20 numbers is zero. Of them, How many of them may be greater than zero, at the most?
Options:
A)3
B)1
C)0
D)19
E)20
Rationale: Average of 20 numbers = 0
Sum of 20 numbers / 20=0
=> Sum of 20 numbers = 0
Hence at the most, there can be 19 positive numbers.
(Such that if the sum of these 19 positive numbers is x, 20th number will be -X)
ANSWER:C
Answer: C
Question: Three sets of 90, 50 and 70 students appeared for an examination and the pass percentage was 50, 90 and 70 respectively. the pass percentage of the whole set is
Options:
A)69.19%
B)66.19%
C)66.29%
D)65.19%
E)68.19%
Rationale: Explanation:
total passed student =45+45+49=139
139 is 66.19% of210
ANSWER:B
Answer: B
Question: Ram sold two bicycles, each for Rs.990. If he made 10% profit on the first and 10% loss on the second, what is the total cost of both bicycles?
Options:
A)2000
B)3377
C)2997
D)26790
E)28781
Rationale: (10*10)/100 = 1%loss
100 --- 99
? --- 1980 => Rs.2000
Answer: A
Answer: A
Question: Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 24624, how much amount per month would he have spent on clothes and transport?
Options:
A)4038
B)8076
C)2052
D)4845.6
E)None of these
Rationale: ∵ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month
∵ Amount, spent on clothes and transport
= 24624⁄12 = 2052
Answer C
Answer: C
Question: If 3 girls can do 3 times of a particular work in 3 days, then, 7 girls can do 7 times of that work in
Options:
A)3 days
B)4 days
C)5 days
D)7 days
E)8 days
Rationale: That is, 1 girl can do one time of the work in 3 days.
Therefore, 7 girls can do 7 times work in the same 3 days itself.
A)
Answer: A
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is:
Options:
A)40
B)80
C)120
D)200
E)None
Rationale: EXPLANATION
Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x.
So, 60x = 2400 or x = 40.
The numbers are (3 x 40), (4 x 40) and (5 x 40).
Hence, required H.C.F. = 40.
Answer A
Answer: A
Question: For every $10 that a billionaire spends, a millionaire spends the equivalent of 20 cents. For every $4 that a millionaire spends, a yuppie spends the equivalent of $1. The ratio of money spent by a yuppie, millionaire, and billionaire can be expressed as
Options:
A)1 : 4 : 400
B)1 : 4 : 100
C)20 : 4 : 1
D)100 : 4 : 1
E)400 : 4 : 1
Rationale: B.........M........Y
10.....0,20......Y
B.........4........1
What I did first was to turn 0.20 to 2 (by multiplying by 10), so that it is easy to find the LCM. This led me to this:
B.........M........Y
100.....2.........Y
B........40......10
Then I multiplied every row by 40 (the LCM of 2 and 40), which led me to this:
B.........M........Y
1000...40.......10
Then I got rid of the extra zero, and in the correct order this is Y:M:B=1:4:100
ANS B
Answer: B
Question: A train running at the speed of 40 km/hr crosses a pole in 27 seconds. What is the length of the train?
Options:
A)250
B)300
C)350
D)400
E)450
Rationale: Speed=(40 * 5/18) m/sec = (100/9) m/sec Length of the train = (Speed x Time) = (100/9 *29 ) m
= 300 m.
Answer: B
Answer: B
Question: From a certain number of people who attended an interview, y people were selected. If instead, y+2 are selected, the number of possible selections would be the same. Which of the following cannot be the value of y if at least 2 interviews were conducted everyday and the interviews were completed in 4 days?
Options:
A)6
B)10
C)5
D)2
E)8
Rationale: At least 2 interviews a day, so minimum 8 interviews in four days. Thus at least a total of 8 candidates should be there.
Let, total candidates = n
according to the question,
nCx = nC(y+2)
or, nCn-y = nCy+2 [nCr = nCn-r]
or, n-y = y+2
so, n = 2y+2
Remember total least number should be 8? So below 8 we can't expect anything.
Put y=2, then n=6 that is unacceptable.
so y is not equal to 2 .
Answer:D
Answer: D
Question: A set of numbers has the property that for any number x in the set, x+3 is also in the set. If -3 is in the set, which of the following must also be in the set
1. -6
2. 0
3. 6
Options:
A)1 only
B)2 only
C)1 and 2 only
D)2 and 3 only
E)1,2 and 3
Rationale: If X is in the set than X+ 3 is also in the set
If -3 in the set than
-3+3= 0 is also in the set
Since + 3 is Present, 3 + 3= 6 Is also present in the set .
Therefore Answer: D
Answer: D
Question: A retail appliance store priced a video recorder at 20 percent above the wholesale cost of $200. If a store employee applied the 5 percent employee discount to the retail price to buy the recorder, how much did the employee pay for the recorder?
Options:
A) $198
B) $228
C) $220
D) $230
E) $240
Rationale: Wholesale cost of video recorder = 200 $
Video recorder was priced at 20 percent above 200 = 240 $
% discount given by store employee = 5
Emlpoyee paid = .95 * 240 = 228 $
Answer B
Answer: B
Question: Eight years ago, Ajay's age was 4/3 times that of Vijay. Eight years hence, Ajay's age will be 6/5 times that of Vijay. What is the present age of Ajay?
Options:
A)11
B)40
C)38
D)27
E)12
Rationale: Explanation:
Let the present ages of Ajay and Vijay be 'A' and 'V' years respectively.
A - 8 = 4/3 (V - 8) and A + 8 = 6/5 (V + 8)
3/4(A - 8) = V - 8 and 5/6(A + 8) = V + 8
V = 3/4 (A - 8) + 8 = 5/6 (A + 8) - 8
=> 3/4 A - 6 + 8 = 5/6 A + 20/3 - 8
=> 10 - 20/3 = 10/12 A - 9/12 A
=> 10/3 = A/12 => A = 40.
Answer: B
Answer: B
Question: A bus started its journey from Mumbai and reached Pune in 30 min with its average speed of 60 km/hr. If the average speed of the bus is increased by 10 km/hr, how much time will it take to cover the same distance?
Options:
A)28 min 30 sec
B)25 min 42 sec
C)25 min 40 sec
D)25 min 43 sec
E)30 min 00 sec
Rationale: Sol. Distance between Ramgarh and Devgarh =(60*30/60=30
Average speed of the bus is increased by 10 km/hr then the
speed of the bus = 70km/hr
Required time = 30*60/70= 25min 42sec
B
Answer: B
Question: Robert is travelling on his cycle andhas calculated to reach point A at 2 PM. if he travels at 10 kmph, he will reach there at 12Pm if he travels at 15 kmph. At what speed must he travel to reach A at 1 PM?
Options:
A)8 kmph
B)10 kmph
C)12 kmph
D)14 kmph
E)16 kmph
Rationale: Let the distance travelled by x km.
Then,	x	-	x	= 2
10	15
3x - 2x = 60
x = 60 km.
Time taken to travel 60 km at 10 km/hr = 60	hrs	= 6 hrs.
10
So, Robert started 6 hours before 2 P.M. i.e., at 8 A.M.
Required speed = 60	kmph.	= 12 kmph.
5
C
Answer: C
Question: John has a certain number of marbles in his pocket. He is able to divide his marbles equally to five of his friend but while trying to divide that same amount of marbles to seven of his other friend he found out that some marbles are left out. What could be the number of marbles that John have?
Options:
A)70
B)21
C)50
D)35
E)105
Rationale: since John was able to divide his marble equally to 5 of his friend but not to 7 of his friend so the total marbles that he has should be divisible by 5 but not by 7.
75, 35 and 105 are all divisible by 5 and 7--- ruled out
we are now left with 21 and 50, here 21 is again divisible by 7-- wrong again.
The answer has to be 50. [ divisible by 5 but not by 7 ]
answer: (C)
Answer: C
Question: If x is positive and y is negative, which of the following must be true?
Options:
A)The product of x and y is positive
B)The sum of x and y is positive
C)The sum of x and y is negative
D)The difference of x and y is positive
E)The sum of x^2 and y^2 is positive
Rationale: To solve this question, we need to remember the following things:
-ve * -ve = +ve
+ve *+ve = +ve
-ve * +ve = -ve
Given that x = +ve and y = -ve
Checking the options:
A. The product of x and y is positive. FALSE
B. The sum of x and y is positive.
Cannot be said. This will depend on the values of x and y
C. The sum of x and y is negative
This will depend on the values of x and y
D. The difference of x and y is positive
This will depend on the values of x and y
E. The sum of x^2 and y^2 is positive
This will always be true as the square of any number is always +ve
And the summation of 2 positive numbers will always be positive.
Correct Option: E
Answer: E
Question: What is the perimeter, in meters, of a rectangular garden 8 meters wide that has the same area as a rectangular playground 16 meters long and 12 meters wide?
Options:
A)48
B)56
C)64
D)76
E)192
Rationale: Say Length of garden is L meters.
Then (L*8) = 16 * 12 [Given area is same. Area= L * B]
Therefore L works out to 24 meters.
Perimeter of Garden = 2* (24+8) = 64 meter.
Answer is C
Answer: C
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 40, the dividend is?
Options:
A)3320
B)4040
C)4330
D)4334
E)4336
Rationale: Divisor = (5 * 40) = 200
= 10 * Quotient = Divisor
=> Quotient = 200/10 = 20
Dividend = (Divisor * Quotient) + Remainder
Dividend = (200 * 20) + 40 = 4040
B
Answer: B
Question: A can do a piece of work in 15 days and B can do it in 15 days and C can do it 20 days. They started the work together and A leaves after 2 days and B leaves after 4 days from the beginning. How long will work lost?
Options:
A)15
B)10
C)12
D)11
E)13
Rationale: 2/15 + 4/15 + x/20 = 1
x = 12 Answer: C
Answer: C
Question: If |5x−6|=|x+20|, which of the following could be a value of x?
Options:
A)6
B)-7/3
C)−13/3
D)-6
E)13/2
Rationale: 5x - 6 = -x + 20 or 5x - 6 = x - 20
6x = 26 or 4x = -24
x = 13/3 or x = -6
Answer: D
Answer: D
Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be
Options:
A)12 years
B)20 years
C)25 years
D)28 years
E)None
Rationale: Solution
Let the present ages of son and father be x and (60 - x) years respectively.
Then,	(60 - x) - 6 = 5(x - 6)
= 54 - x = 5x - 30
‹=›6x = 84
‹=›x= 14.
∴Son's age after 6 years = (x + 6) = 20 years.
Answer B
Answer: B
Question: If there are four distinct pairs of brothers and sisters, then in how many ways can a committee of 3 be formed and NOT have siblings in it?
Options:
A)8
B)24
C)32
D)56
E)192
Rationale: let AABBCCDD is the group with same letter representing a sibling pair.
total # ways to select 3 from 8 is 8C3=56
Qtn: committee of 3 NOT having siblings in it = Total (56) - committee of 3 with siblings in it
committee of 3 with siblings = select 2As and one from rem. 6. This can be done in 4 ways as 4 different letters A,B,C and D
= 4 * (2C2*6C1) = 24
Hence Answer = 56-24 = 32
ANS:C
Answer: C
Question: Having scored 97 runs in the 19th inning, a cricketer increases his average score by 4. What will be his average score after 19 innings?
Options:
A)28
B)27
C)26
D)22
E)25
Rationale: Explanation :
Let the average score of the first 18 innings be n
18n + 97 = 19(n+4)=> n = 21
So, Average score after 19th innings = x+4 =25.
Answer : E
Answer: E
Question: A question paper has 2parts, A & B, each containing 10 questions. If a student has to choose 8 from part A &5 from part B, in how many ways can he choose the questions?
Options:
A)1100
B)1200
C)1235
D)1354
E)1140
Rationale: There 10 questions in part A out of which 8 question can be chosen as = 10C8.
Similarly, 5 questions can be chosen from 10 questions of Part B as = 10C5.
Hence, total number of ways,
=10C8*10C5
=[10!/(2!8!)]*[10!/(5!*5)]
= {10*9/2}*{10*9*8*7*6/(5*4*3*2*1)}
= 1140.
E
Answer: E
Question: A rower can row 7 km/h in still water. When the river is running at 1 km/h, it takes the rower 1 hour to row to Big Rock and back. How many kilometers is it to Big Rock?
Options:
A)3.19
B)3.28
C)3.35
D)3.43
E)3.56
Rationale: Let x be the distance to Big Rock.
time = x/6 + x/8 = 1
x = 48/14 = 3.43 km
The answer is D.
Answer: D
Question: What is the 6th digit to the right of the decimal point in the decimal equivalent of 16/45?
Options:
A)5
B)12
C)2
D)35
E)4
Rationale: 16/45 = 0.3555....
35 is non-terminating repeating decimal.
The 22nd digit to the right of decimal point will be 5.
Answer A
Answer: A
Question: An order was placed for the supply of a carpet whose breadth was 6 m and length was 1.44 times the breadth. What be the cost of a carpet whose length and breadth are 40% more and 25% more respectively than the first carpet. Given that the ratio of carpet is Rs. 45 per sq. m ?
Options:
A)Rs. 4082.40
B)Rs. 1024.21
C)Rs. 2810.6
D)Rs. 3214
E)NONE OF THESE
Rationale: Explanation:
Length of the first carpet = (1.44)(6) = 8.64 cm
Area of the second carpet = 8.64(1 + 40/100) 6 (1 + 25/100)
= 51.84(1.4)(5/4) sq m = (12.96)(7) sq m
Cost of the second carpet = (45)(12.96 x 7) = 315 (13 - 0.04) = 4095 - 12.6 = Rs. 4082.40
ANSWER IS A
Answer: A
Question: Meera purchased two three items from a shop. Total price for three items is Rs.8200/- She have given Rs. 10000/- What is the balance amount meera got?
Options:
A)1800
B)1200
C)1650
D)800
E)750
Rationale: Total cost of Items : 8200/-
amount Paid : 10000/-
Balance receivable : 10000- 8200 = 1800/-
Answer is A
Answer: A
Question: In an increasing sequence of 10 consecutive integers, the sum of the first 5 integers is 540. What is the sum of the last 5 integers in the sequence?
Options:
A) 585
B) 580
C) 575
D) 570
E) 565
Rationale: All 5 integers are 5 numbers larger than in the first sum (eg. 1 becomes 6, 2 7...). 5*5=25+540=565
E
Answer: E
Question: When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number?
Options:
A)228
B)103
C)286
D)122
E)102
Rationale: Explanation:
Let the number be x
x2 - 732 = 5280
x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609
= 10000 + 2(100)(3) + 32 = (100 + 3)2
x = 100 + 3 = 103.
Answer: B
Answer: B
Question: Sunil invested $ 2600 fir 3 years and $ 1200 for 5 years at the same rate of Simple Interest. If the total interest from these investments is $ 930, what is the rate of interest?
Options:
A)2 3/4%
B)5 1/3%
C)5 1/2%
D)6 3/4%
E)3 2/4%
Rationale: (2600x3xR)/100+(1200x5xR)/100=930
138R=930
R= 6 3/4%
Answer is D
Answer: D
Question: There are 12 cans in the refrigerator. 7 of them are red and 5 of them are blue. In how many ways we can remove 10 cans so that at least one red and at least one blue cans to remain the refrigerator.
Options:
A)460
B)490
C)493
D)35
E)445
Rationale: Ways to pick 2 cans so that at least one red and at least one blue cans to remain the refrigerator =
total ways to pick 2 can out of 12 - ways to pick 2 red out of 7 red - ways to pick 2 blue out of 5 blue
12C2âˆ’7C2âˆ’5C2=66âˆ’21âˆ’10=35
ANSWER:D
Answer: D
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Options:
A)3 years
B)4 years
C)6 years
D)7 years
E)8 years
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
B)
Answer: B
Question: When divided by 5, x has a remainder of 3 and y has a remainder of 1. Which of the following could be the remainder when x + y is divided by 10?
Options:
A)6
B)7
C)8
D)9
E)0
Rationale: x = 5k+3 and y = 5j+1
x+y = 5(j+k) + 4
When divided by 10, the remainder is either 4 or 9.
The answer is D.
Answer: D
Question: If (2 to the x) - (2 to the (x-2)) = 3 (2 to the 5), what is the value of x?
Options:
A)7
B)11
C)13
D)15
E)17
Rationale: (2 to the power x) - (2 to the power (x-2)) = 3 (2 to the power 5)
2^x - 2^(x-2) = 3. 2^5
Hence x = 7.
Answer is A
Answer: A
Question: How many words can be formed by using all letters of the word “QUADRIC”
Options:
A)1200
B)5040
C)4050
D)3440
E)1550
Rationale: The word QUADRIC contains 7 different letters.
Required number of words = 7p7 = 7! = (7x6x5x4x3x2x1) = 5040
Answer B.
Answer: B
Question: Venus travels around the sun at a speed of approximately 21.9 miles per second. The approximate speed is how many miles per hour?
Options:
A)64,420
B)78,840
C)83,160
D)88,970
E)94,320
Rationale: 21.9 * 3600 = 78,840
The answer is B.
Answer: B
Question: What is the ratio of 3/7 to the product 2*(7/3)?
Options:
A)3:7
B)9:98
C)3:21
D)1:7
E)3:49
Rationale: 3/7 / 14/3 = 9/98...
IMO option B.
Answer: B
Question: Which of the following is closest in value to (9^8)-(9^2)?
Options:
A)9^9
B)9^8
C)9^7
D)9^6
E)9^5
Rationale: 9^8 is much larger number than 9^2 and as we need approximate value then it's pretty much negligible in this case, so: (9^8)-(9^2) = ~9^8.
Answer: B.
Similar questions to practice:
Hope it helps.
Answer: B