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mathematics
|
In a race, A beats B by 15 metres and C by 29 metres. If B and C run over the course together, B wins by 15 metres. What is the length of the course?
|
[
"225m",
"120m",
"220m",
"160m",
"180m"
] |
Explanation:
Let X be the length of the course
according to the question,
A beats B by 15 metres and C by 29 metres
Applying this,
If A runs X metres, B runs (X-15) and C runs ( X-29) metres.
B and C together run, B runs X metres and C runs (X-15)
=> If B runs 1 metre, C runs X-15/X
=> B runs X-15 m, C runs (X-15/x) * (X-15)
APPLYING THIS,
X-29 = (X-15)(X-15) / X
Solving,
X2 -29X= X2 – 30 X + 225
X = 225
Thus, length of the course is 225 metres.
ANSWER A
The answer is: A
|
A
|
mathematics
|
A contractor agreeing to finish a work in 150 days, employed 75 men each working 8 hours daily. After 90 days, only 2/7 of the work was completed. Increasing the number of men by ________ each working now for 10 hours daily, the work can be completed in time.
|
[
"322 men",
"232 men",
"838 men",
"539 men",
"150 men"
] |
One day’s work = 2 / (7 * 90)
One hour’s work = 2 / (7 * 90 * 8)
One man’s work = 2 / (7 * 90 * 8 * 75)
The remaining work (5/7) has to be completed within 60 days, because the total
number of days allotted for the project is 150 days.
So we get the equation
(2 * 10 * x * 60) / (7 * 90 * 8 * 75) = 5/7 where x is the number of men
working after the 90th day.
We get x = 225
Since we have 75 men already, it is enough to add only 150 men.
Answer:E
The answer is: E
|
E
|
mathematics
|
In what time will a train 100 m long cross an electric pole, it its speed be 90 km/hr?
|
[
"2.5 sec",
"2.8 sec",
"8.5 sec",
"2.2 sec",
"4 sec"
] |
Speed = 90 * 5/18
= 25 m/sec
Time taken = 100/25
= 4 sec.
Answer:E
The answer is: E
|
E
|
mathematics
|
Jill invests $10000 in an account that pays an annual rate of 3.96%, compounding semi-annually. Approximately how much does she have in her account after two years?
|
[
"$10079.44",
"$10815.83",
"$12652.61",
"$14232.14",
"$20598.11"
] |
Solution: first of all, notice the magic word “approximately” — the test-writer is letting us know estimation is perfectly fine. Furthermore, the answer choices are nicely spread out, which will facilitate estimating.
OK, get ready for some fast & furious estimation. The interest rate 3.96% is an ugly number, so I’m going to approximate that as 4%. It compounds semiannually, so that means that there’s 2% every six months, and that happens four times in two years. Well, 2% of $10000 is $200. If you get $200, or a little more, on four occasions, that’s a little more than $800 in interest. We expect an answer slightly higher than $10800, so of course (B) is just right.
Notice, I estimated so that everything up until the last sum was single-digit math. Single-digit calculations are a good standard for which to strive when you are practicing estimation.
By the way, if you find the bank that will do answer (E), double your money in only two years, that’s terrific, but it probably is something wildly illegal, a Ponzi scheme or worse! In the real world, that just doesn’t happen. On word problems, especially in financial situations, you should always have your antenna up for what’s realistic or unrealistic.
answer (B)
The answer is: B
|
B
|
mathematics
|
A and B go around a circular track of length 300 m on a cycle at speeds of 18 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
|
[
"120 sec",
"198 sec",
"60 sec",
"665 sec",
"276 sec"
] |
Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 300/ (90 * 5/18) , 300/ (54 * 5 /18) }
= LCM (12, 20) = 60 sec.
Answer:C
The answer is: C
|
C
|
mathematics
|
A company selected 250 zip codes in Northeastern, Florida, Arizona and California in order to mail a product catalog. The number of Northeastern zip codes was twice Florida's, and four times Arizona's, and 4/3 California's. 450,000 catalogues were mailed to California and 25% resulted in product orders. What is the ratio of the number of orders to the number of California's zip codes?
|
[
"a) 500",
"b) 750",
"c) 1,000",
"d) 1,250",
"e) 1,500"
] |
Since N = 2F, no of Florida zip codes (F) will be N/2.
Since N = 4A, no of Arizona zip codes (A) will be N/4
Since N = (4/3)C, no of California zip codes (C) will be 3N/4
N + N/2 + N/4 + 3N/4 = 5N/2 = 250
N = 100
C = 3N/4 = 75
No of orders is 25% of 450,000 = 112,500
So required ratio = 112,500/75 = 1500
Answerr E
The answer is: E
|
E
|
mathematics
|
A driver took a trip consisting of three segments at three different speeds. The driver drove a distance of (3D) at a speed of (2V), then a distance of (7D) at a speed of (3V), then a distance of D at a speed of (6V). In terms of D and V, what was the total time of the trip?
|
[
"3D/V",
"4D/V",
"5D/V",
"6D/V",
"7D/V"
] |
The total time of the trip was:
3D/2V + 7D/3V + D/6V =
18D/12V + 28D/12V + 2D/12V =
48D/12V = 4D/V
The answer is B.
The answer is: B
|
B
|
mathematics
|
What is the area of square field whose side of length 5 m?
|
[
"80 sq m",
"26 sq m",
"25 sq m",
"45 sq m",
"96 sq m"
] |
5 * 5
= 25 sq m
Answer: C
The answer is: C
|
C
|
mathematics
|
A football player scores 5 goals in his fifth match thus increasing his average goals score by 0.2. The total number of goals in his 5 matches would be
|
[
"14",
"16",
"18",
"10",
"21"
] |
While this question can be solved with a rather straight-forward algebra approach (as the other posters have noted), it can also be solved by TESTing THE ANSWERS. One of those numbers MUST be the total number of goals...
From a tactical standpoint, it's best to TEST either Answer B or Answer D, so if the answer is not correct, then you would have a gauge for whether you should gohigherorlowerwith your next TEST.
Here, I'll start with Answer E =21 goals
If....
Total goals = 21 goals
5th game = 5 goals
1st 4 games = 16 goals
Avg. for 1st 4 games = 16/4 = 4 goal/game
Avg. for all 5 games = 21/5 = 4.2 goals/game
This is an EXACT MATCH for what we're told in the prompt, so Answer E MUST be the answer.
The answer is: E
|
E
|
mathematics
|
What is the diffference between the place value and face value of 7 in the numeral 9751?
|
[
"691",
"692",
"693",
"694",
"695"
] |
place value of 7 = 7 * 100 = 700
face value of 7 = 7
700 - 7 = 693
C
The answer is: C
|
C
|
mathematics
|
For what value of x, is |x – 3| + |x + 1| + |x| = 11?
|
[
"0",
"3",
"-3",
"4",
"-2"
] |
For what value of x, is |x – 3| + |x + 1| + |x| = 11?
It's easiest just to plug in answer choices:
(C): -3
|x – 3| + |x + 1| + |x| = 11?
|-3 - 3| + |-3 + 1| + |-3| = 11?
|6| + |2| + |3| = 11
(C)
The answer is: C
|
C
|
mathematics
|
The probability that event A occurs is 0.4, and the probability that events A and B both occur is 0.25. If the probability that either event A or event B occurs is 0.6, what is the probability that event B will occur?
|
[
"0.05",
"0.15",
"0.45",
"0.5",
"0.55"
] |
P(A or B) = P (A) + P(B) - p(a n b)
0.6= 0.4 + P(B) - 0.25
P(B) = 0.45
ANSWER:C
The answer is: C
|
C
|
mathematics
|
If p and q are two different odd prime numbers, such that p < q, then which of the following must be true?
|
[
"(2p + q) is a prime number",
"p + q is divisible by 4",
"q - p is divisible by 4",
"(p + q + 1) is the difference between two perfect squares of integers",
"p2+q2 is the difference between two perfect squares of integers"
] |
1. (2p + q) for sure is an odd number , but may or may not be a prime number .
Eg - if we take 3 and 5 as p and q resp, we get 11, which is a prime number.
But if we take 7 and 11, we get 25, which is not a prime number.
2. p + q for sure gives us an even number. It may or may not be divisible by 4.
Eg - (7 + 5) = 12 , which is divisible by 4. But (11 + 7) = 18 , not divisible by 4
3. Same way as 2nd.
4. (p + q + 1) gives us an odd number.
Lets see the trend of difference between squares of consecutive integers.
2^2 - 1^2 = 3
3^2 - 2^2 = 5
4^2 - 3^2 = 7
5^2 - 4^2 = 9
6^2 - 5^2 = 11 and so on.
The trend is : The difference between squares of consc. integers is always odd number. And it covers all the odd numbers.
However , when we don't take consecutive integers, this trend is not followed.
Eg : 5^2 - 3^2 = 16 , which is an even number
3^2 - 1^2 = 8 , again not an odd number
Hence : Any odd number can be expressed as the difference of the squares of integers.
5. (p^2 + q^2) gives an even number.
ANSWER:D
The answer is: D
|
D
|
mathematics
|
Sum of the squares of three numbers is 116 and the sum of their products taken two at a time is 70. Find the sum?
|
[
"14",
"15",
"16",
"17",
"18"
] |
(a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 116 + 2* 70
a + b + c = √256 = 16
C
The answer is: C
|
C
|
mathematics
|
In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (3,-1), (3, 8), (12, 2), (12,-7)?
|
[
"69",
"75",
"81",
"87",
"93"
] |
By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Area = 1/2 × (9 + 9) × 9 = 81.
The answer is C.
The answer is: C
|
C
|
mathematics
|
A boy has Rs. 720 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
|
[
"90",
"110",
"140",
"135",
"120"
] |
Let number of notes of each denomination be x.
Then x + 5x + 10x = 720
16x = 720
x = 45
Hence, total number of notes = 3x = 135
D
The answer is: D
|
D
|
mathematics
|
x varies inversely as square of y. Given that y=3 for x=1. The value of x for y = 2 will be equal to:
|
[
"3",
"6",
"1/9",
"1/3",
"9/4"
] |
Explanation :
Solution: Given x = k/y^2, where k is constant. Now, y=3 and x =1 gives k = 9.
.'. x = 9/y^2
=> x =9 /2^2 = 9/4
Answer : E
The answer is: E
|
E
|
mathematics
|
A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 102. What was the number he chose?
|
[
"120",
"335",
"784",
"217",
"210"
] |
Let x be the number he chose, then
2*x*138=102
2x=240
x=120
correct answer A
The answer is: A
|
A
|
mathematics
|
Insert the missing number
4, -8, 16, -32, 64, (....)
|
[
"128",
"-128",
"192",
"-132",
"0"
] |
4*-2=-8
-8*-2=16
16*-2=-32
-32*-2=64
64*-2=-128
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Two trains, each 100 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is?
|
[
"29",
"29",
"60",
"19",
"12"
] |
Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/8 = 3x => x = 25/3.
So, speed of the faster train = 50/3 = 50/3 * 18/5
= 60 km/hr.
Answer:C
The answer is: C
|
C
|
mathematics
|
If x = y+3+4.5x and y = x+33, what is the value of x/y ?
|
[
"-6/5.",
"-8/25",
"1/4.",
"5/6.",
"1.5."
] |
(1) x = y + 3 + 4.5x
Substitute y for y = x + 33 (Eq. we are given)
x = x + 33 + 3 + 4.5x
Combine like terms
x = 5.5x +36 --> -4.5x = 36 --> x = -8
(2) y = x + 18
Substitute x for x = -8
y = (-8) + 33 = 25
(3) x/y = ?
Substitute x and y we found above
x/y = (-8) / (25) =-8/25
My answer: B
The answer is: B
|
B
|
mathematics
|
A credit card number has 6 digits (between 1 to 9). The first two digits are 12 in that order, the third digit is bigger than 4, the forth is divisible by 3 and the fifth digit is 3 times the sixth. How many different credit card numbers exist?
|
[
"27",
"36",
"72",
"112",
"45"
] |
{1}{2}{greater than 6}{divisible by 3}{3x}{x}:
The third digit can take 5 values: 5,6,7, 8, or 9.
The fourth digit can take 3 values: 3, 6, or 9.
The fifth and sixth digits can take 3 values: 31, 62, or 93.
Total = 5*3*3 = 45.
Answer: E.
The answer is: E
|
E
|
mathematics
|
A and B go around a circular track of length 600 m on a cycle at speeds of 36 kmph and 54 kmph. After how much time will they meet for the first time at the starting point?
|
[
"120 sec",
"176 sec",
"178 sec",
"187 sec",
"189 sec"
] |
Time taken to meet for the first time at the starting point
= LCM { length of the track / speed of A , length of the track / speed of B}
= LCM { 600/ (36 * 5/18) , 600/ (54 * 5 /18) }
= LCM (60, 40) = 120 sec.
Answer: A
The answer is: A
|
A
|
mathematics
|
In the graduating class of a certain college, 48 percent of the students are male and 52 percent are female. In this class 50 percent of the male and 20 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old?
|
[
"A)0.9",
"B)0.6",
"C)0.45",
"D)0.3",
"E)0.25"
] |
Percent of students who are 25 years old or older is 0.5*48+0.2*52=~34, so percent of people who are less than 25 years old is 100-3=66.
Answer: B.
The answer is: B
|
B
|
mathematics
|
Find the compound ratio of (2:3), (6:11) and (11:4) is
|
[
"3:2",
"2:1",
"1:1",
"4:5",
"2:3"
] |
Required ratio = 2/3 * 6/11 * 11/4 = 2/1 = 1:1
Answer is C
The answer is: C
|
C
|
mathematics
|
On his first 3 tests, Rajeev received an average score of X points. If on his fourth test, he exceeds his previous average score by 24 points, what is his average score for his first 4 tests?
|
[
"X",
"X+6",
"X+4",
"X+3",
"X+2"
] |
Total of 1st 3 tests= 3X
4th test score = X + 24
Total of all 4 tests = 4X + 24
Average = X + 6
Answer : B
The answer is: B
|
B
|
mathematics
|
What is the tens digit of 6^21?
|
[
"1",
"3",
"5",
"7",
"9"
] |
The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3.
The tens digit of 6^3=216 is 1.
The tens digit of 6^4=...96 is 9.
The tens digit of 6^5=...76 is 7.
The tens digit of 6^6=...56 is 5.
The tens digit of 6^7=...36 is 3 again.
etc...
21 has the form 5n+1, so the tens digit of 6^21 is 5.
The answer is C.
The answer is: C
|
C
|
mathematics
|
At The KHOOL Company, high quality and low quality solar reflecting sunglasses are made, where 70 percent of the sunglasses made are high quality and 25 percent are low quality (defective sunglasses are tossed away into the recycle bin, but must be counted as product produced). If there are 50 sunglasses made per day that are defective and can't be sold as low or high quality sunglasses, how many sunglasses does The KHOOL Company make total per day?
|
[
"100",
"1,800",
"1,090",
"200",
"1,000"
] |
Let the total number of sunlasses produced be x
% of high quality sunglasses = 70%
% of low quality sunglasses = 25%
% of sunglasses defective = 100% - 95% = 5%
But this number is given as 50
so 5% of x = 50 and x = (50)(100/5))
x = 180
Therefore there a total of 1,000 sunglasses made per day.
Correct answer - E
The answer is: E
|
E
|
mathematics
|
If x^2 = 111, which of the following is closest to a potential value of x?
|
[
"-127",
"-11",
"12",
"13",
"131"
] |
Here the thing we must not forget is that X^even has two potential solutions
=> x =+- √111 => +- 11
this value is closer to -11
Hence B is correct.
The answer is: B
|
B
|
mathematics
|
Three hundred students at College Q study a foreign language. Of these, 160 of those students study French, and 190 study Spanish. If at least 90 students who study a foreign language at College Q study neither French nor Spanish, then the number of students who study Spanish but not French could be any number from
|
[
"30 to 50",
"40 to 100",
"60 to 100",
"60 to 110",
"70 to 110"
] |
160 students study French
140 students do not study French
190 students study Spanish
110 students do not study Spanish
90 students study neither French nor Spanish
140-110=30
140-90=50
A. 30 to 50
The answer is: A
|
A
|
mathematics
|
A certain company had a total annual expenditure of 2.55∗10^7 on employee salaries last year. If the company employed 425 people, what was the average employee salary?
|
[
"$60,000",
"$25,000",
"$35,000",
"$40,000",
"$45,000"
] |
Given: Total annual expenditure of 2.55∗10^7 on employee salaries
Total employees = 425
Observe that 425*6 = 2550
Therefore try to bring the numerator in terms of 2550
Average salary = (2550*10^4) /425 = 6*10^4 = 60,000
Option A
The answer is: A
|
A
|
mathematics
|
Louie takes out a three-month loan of $4000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
|
[
"A)333",
"B)383",
"C)1608",
"D)433",
"E)483"
] |
Here's the calculation for that case, assume monthly payment is X.
After 1st month: (4000)(1.1)-X = 4400-X
After 2nd month: (4400-X)(1.1)-X = 4840-2.21X
After 3rd month: (4840-2.21X)(1.1)-X = 5324-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
5324-3.31X = 0
X = 5324/3.31 = 1608.45
Answer C
The answer is: C
|
C
|
mathematics
|
Kiran had 85 currency notes in all , some of which were of Rs.100 denaomination and the remaining of Rs.50 denomination the total amount of all these currency note was Rs.5000.how much amount did she have in the denomination of Rs.50?
|
[
"rs.2500",
"rs.3500",
"rs.1500",
"rs.4500",
"rs.5500"
] |
100X +50 (85-X) =5000
on solving:
x=15
100-x=no. of 50 notes = 70
amount =70*50= rs.3500
ANSWER:B
The answer is: B
|
B
|
mathematics
|
A corporation triples its annual bonus to 50 of its employees. What percent R of the employees’ new bonus is the increase?
|
[
"50%",
"662⁄3%",
"100%",
"200%",
"300%"
] |
R of the employees’ new bonus is the increase Hence B.
The answer is: B
|
B
|
mathematics
|
A bowl was filled with 10 ounces of water, and 0.008 ounce of the water evaporated each day during a 50-day period. What percent of the original amount of water evaporated during this period?
|
[
"0.004%",
"0.04%",
"0.40%",
"4%",
"40%"
] |
Total amount of water evaporated each day during a 50-day period = .008 * 50
=.008 * 100/2
= .8/2
= .4
percent of the original amount of water evaporated during this period = (.4/10) * 100%
= 4 %
Answer D
The answer is: D
|
D
|
mathematics
|
Nine children — A, B, C, D, E, F, G, H, and I — are going to sit in nine chairs in a row. Child C must be somewhere to the left of child D. How many possible configurations are there for the children?
|
[
"155,880",
"164,770",
"173,660",
"181,440",
"192,550"
] |
The number of ways to seat 9 people is 9! = 362,880.
Child C will sit to the left of Child D in exactly half of these arrangements.
The total number of possible arrangements is 362,880/2 = 181,440
The answer is D.
The answer is: D
|
D
|
mathematics
|
Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
|
[
"4!",
"8!",
"9!",
"10!",
"12!"
] |
Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
The answer is: B
|
B
|
mathematics
|
A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 30% impurities to the product. Find the net profit percentage of the dealer?
|
[
"44%",
"40%",
"50%",
"56.25%",
"37.5%"
] |
The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.
It means that he is selling $4 worth of product for $5.
The dealer then further added 30% impurities to the product.
It means that he is selling $5 worth of product for $5.5.
So his profit is $5.5-$4 = $1.5
and his profit percent is
(1.5/4)*100 = 37.5%
Answer:- E
The answer is: E
|
E
|
mathematics
|
Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is:
|
[
"3776",
"2687",
"8400",
"2688",
"2671"
] |
Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23 = Rs. 8400.
Answer: C
The answer is: C
|
C
|
mathematics
|
How many integer values Q are there for x such that 1 < 3x + 5 < 17?
|
[
"Two",
"Three",
"Four",
"Five",
"Six"
] |
1 < 3x + 5 < 17
=> -4 < 3x < 12
=> -4/3 < x < 4
x can take integer values Q=-1,0 , 1 , 2 , 3
Answer D
The answer is: D
|
D
|
mathematics
|
A train 210 metres long is moving at a speed of 25 kmph. It will cross a man coming from the opposite direction at a speed of 2 km per hour in :
|
[
"28 sec",
"32 sec",
"36 sec",
"38 sec",
"40 sec"
] |
Relative speed = (25+2) km/hr = 27 km/hr
= (27×5/18) m/sec = 15/2 m/sec.
Time taken by the train to pass the man =(210×2/15) sec=28 sec
ANSWER :A
The answer is: A
|
A
|
mathematics
|
Abigail has $460 in 5-and 10-dollar bills only. If she has fewer 10-than 5-dollar bills, what is the least possible number of 5-dollar bills she could have?
|
[
"32",
"30",
"29",
"28",
"27"
] |
5g + 10h = 460
g > h
Pick an easy number to work with.
suppose g=30.
Then you have 150.
You need another 310 and that means you need h=31 which is greater than g.
Therefore, g > 30.
The only answer choice where g > 30 is if g = 32.
A is the answer.
The answer is: A
|
A
|
mathematics
|
In a graduating class of 232 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number R and the smallest possible number of students that could have taken both geometry and biology?
|
[
"144",
"119",
"113",
"88",
"31"
] |
OFFICIAL SOLUTION:
First of all, notice that since 144 took geometry and 119 took biology, then the number of students who took both geometry and biology cannot be greater than 119.
{Total} = {geometry} + {biology} - {both} + {neither};
232 = 144 + 119 - {both} + {neither};
{both} = 31 + {neither}.
{both} is minimized when {neither} is 0. In this case {both} = 31.
The greatest possible number R of students that could have taken both geometry and biology, is 119.
Thus, the answer is 119 - 31 = 88.
Answer: D.
The answer is: D
|
D
|
mathematics
|
Dana borrows 7500 pounds annually for her college education. If Dana gives her parents 5% of that amount back each month, how much will she still owe her parents after four years of college?
|
[
"8000",
"9000",
"10000",
"11000",
"12000"
] |
dana borrows 7500 and returns 5% per month.
so returns 375 per month. and 4500 per year.
so dana owes 7500-4500=3000 per year.
after 4 years she will owe 12000.
Ans (E)
The answer is: E
|
E
|
mathematics
|
A number x is 5 times another number y. The percentage that y is less than x is
|
[
"12.5%",
"87.5%",
"80%",
"11%",
"1%"
] |
Say y=1 and x=5.
Then y=1 is less than x=5 by (5-1)/5*100=4/5*100=80%.
Answer: C.
The answer is: C
|
C
|
mathematics
|
At a certain resort, each of the 39 food service employees is trained to work in a minimum of 1 restaurant and a maximum of 3 restaurants. The 3 restaurants are the family buffet, the dining room, and the snack bar. Exactly 15 employees are trained to work in the family buffet, 18 are trained to work in the dining room, and 12 are trained to work in the snack bar. If 4 employees are trained to work in exactly 2 restaurants, how many employees are trained to work in all 3 restaurants?
|
[
"2",
"3",
"4",
"5",
"1"
] |
39 = 15+ 18 + 12 - 4 - 2x
2x = 15 + 18 + 12 - 4 - 39
= 41 - 39
= 2
x =1
E
The answer is: E
|
E
|
mathematics
|
A car during its journey travels 30 minutes at a speed of 40 kmph, another 45 minutes at a speed of 80 kmph, and 2 hours at a speed of 50 kmph.The average speed of the car is
|
[
"60.07 kmph",
"55.38 kmph",
"50.02 kmph",
"44.02 kmph",
"None of these"
] |
First car travels 30 min at speed of 40 kmph
distance = 40 x 1/2 = 20 m
Then car travels 45 min at a speed of 80 kmph
distance = 45 min at speed of 80 kmph
distance = 80 x 3/4 = 60 m
at last it travels 2 hours at speed of 50 kmph
distance = 50 x 2 = 100 m
Total distance = 20 + 60 + 100 = 180
Total time= 1/2 + 3/4 + 2 = 3.25
Average speed of the car = 180/3.25 = 55.38
ANSWER:B
The answer is: B
|
B
|
mathematics
|
A train 70 m long, running with a speed of 63 km/hr will pass a tree in?
|
[
"140 sec",
"160 sec",
"176 sec",
"150 sec",
"170 sec"
] |
Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 70 * 2/35 = 140 sec
Answer:A
The answer is: A
|
A
|
mathematics
|
A football coach must choose 4 freshers from a team of 12players. How many different ways can the coach choose the freshers?
|
[
"495",
"650",
"729",
"800",
"890"
] |
Choose 4 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{4}}= 495
A
The answer is: A
|
A
|
mathematics
|
If x = -2 and y = -4, what is the value of 5(x-y)^2 - xy ?
|
[
"12",
"13",
"15",
"18",
"22"
] |
x = -2 and y = -4
x-y = -2 - (-4) = -2+4 = 2
x*y = -2 * -4 = 8
Now we apply it in the equation 5(x-y)^2 - xy =5 (2)^2-8
==>5*4 -8 = 20-8 =12
Answer : A
The answer is: A
|
A
|
mathematics
|
Elena purchased Brand X pens for $4.00 apiece and brand Y for $2.20 apiece. If Elena purchased a total of 12 of these pens for $42.00, how many brand X pens did she purchase?
|
[
"4",
"5",
"6",
"7",
"8"
] |
4x+2.8y=42 --> multiply by 2.5 (to get the integers) --> 10x+7y=105 --> only one positive integers solutions x=6 and y=5 (how to solve: 7y must have the last digit of 5 in order the last digit of the sum to be 5).
Answer: C.
The answer is: C
|
C
|
mathematics
|
Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?
|
[
"10",
"25",
"12",
"20",
"30"
] |
Explanation:
Speed of train 1 = 12 m/sec
Speed of train 2 = 8 m/sec
if they travel in opposite direction, relative speed = 12 + 8 = 20 m/sec
distance covered = 120 + 120 = 240 m
time = distance/speed = 240/20 = 12 sec
ANSWER IS C
The answer is: C
|
C
|
mathematics
|
The average age of a husband and a wife is 23 years when they were married FOUR years ago but now the average age of the husband, wife and child is 20 years(the child was born during the interval). What is the present age of the child?
|
[
"7 years",
"9 years",
"6 years",
"4 years",
"5 years"
] |
27 * 2 = 54
20 * 3 = 60
-----------
6 years
Answer: C
The answer is: C
|
C
|
mathematics
|
Mother,her daughter and her grand child weighs 140 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
|
[
"44",
"47",
"48",
"49",
"50"
] |
mother + daughter + child = 140kg
daughter + child = 60kg
mother = 140 - 60 = 80kg
child = 1/5th of mother = (1/5)*80 = 16kg
So now daughter = 140 -(mother + child) = 140 - (80+16) = 44kg
ANSWER:A
The answer is: A
|
A
|
mathematics
|
Reema took a loan of Rs 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest.
|
[
"5%",
"6%",
"7%",
"8%",
"9%"
] |
Explanation:
Let rate = R% then Time = R years.
=>1200∗R∗R /100=432
=>R2=36
=>R=6%
Option B
The answer is: B
|
B
|
mathematics
|
In 1995, there are 28 days in February and there are 365 days in the year. In 1996, there are 29 days in February and there are 366 days in the year. If the date February 12, 1995 is a Wednesday, then which one of the following would the date February 12, 1996 be?
|
[
"Thursday",
"Friday",
"Saturday",
"Sunday",
"Monday"
] |
From the information given, Feb 12, 1996 is 366 days after Feb 12, 1995.
366 days = 52 weeks and 2 more days. Therefore if Feb 12, 1995 is a Wednesday, then Feb 12, 1996 is Wednesday + 2 days = Friday
Answer: B
The answer is: B
|
B
|
mathematics
|
How many multiples of 100 are there between 100 and 1000 (both are inclusive)?
|
[
"2",
"8",
"4",
"5",
"10"
] |
the answer is (1000-100)/100+1=10
Answer is E
The answer is: E
|
E
|
mathematics
|
If the average (arithmetic mean) of the four numbers 3, 25, 52, and (N + 1) is 50, then N =
|
[
"119",
"120",
"121",
"122",
"129"
] |
3+25+52+N+1= 50 x 4 = 200
=>N +81 = 200
=>N=119
Answer A
The answer is: A
|
A
|
mathematics
|
How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
|
[
"30",
"88",
"66",
"44",
"31"
] |
Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer: A
The answer is: A
|
A
|
mathematics
|
The ratio of two quantities is 2 to 5. If each of the quantities is increased by 6, what is the ratio of these two new quantities?
|
[
"2/5",
"5/8",
"7/13",
"22/25",
"It cannot be determined from the information given."
] |
Correct Answer: E
Let x and y be the two quantities such that x/y = 2/5. There is no algebraic operation that can be used to increase x and y each by 3 and determine what happens to the ratio 2/5.
For example, if x = 2 and y = 5, then (x+6)/(y+6) = (2+6)/(5+6) = 8/11. However, if x = 4 and y = 10 (which would still set x/y = 2/5), then (x+6)/(y+6) = (4+6)/(10+6) = 10/16. The ratio of the two new quantities cannot be uniquely determined from the information given, and the correct answer is (E).
The answer is: E
|
E
|
mathematics
|
At a certain college, 80 percent of the total number of students are freshmen. If 60 percent of the fresh-men are enrolled in the school of liberal arts and, of these, 50 percent are psychology majors, what percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
|
[
"25%",
"30%",
"24%",
"28%",
"20%"
] |
Let's say there is a TOTAL of 100students at this college.
80 percent of the total number of students are freshmen.
# of freshmen = 80% of 100 =80
60 percent of the fresh-men are enrolled in the school of liberal arts...
Number of liberal arts freshmen = 60% of 80 = 48
...and, of these, 50 percent are psychology majors...
Number of liberal arts freshmen who are psychology majors = 50% of 48=24
What percent of the students at the college are freshmen psychology majors enrolled in the school of liberal arts?
24/100= 24%
Answer:C
The answer is: C
|
C
|
mathematics
|
If 4f^4 − 41f^2 + 100 = 0, then what is the sum of the two greatest possible values of f ?
|
[
"4",
"9/2",
"7",
"41/4",
"25"
] |
just forget about the value of f^4 for the moment and let f^2= X. (its better to work with power of 2 than 4)
now we have equation as 4x^2 -41x +100 =0, factoring them gives us 4X^2 -16x -25x +100 =0. which can be solved as (4x-25)(x-4) , so x= 4 and 25/4.
so f^2 = 4 and 25/4
so f= +2 and minus 2 and +5/2 and minus 5/2
The two greatest values are +2 and +5/2. so their sum 2+5/2 =9/2 = B
The answer is: B
|
B
|
mathematics
|
Diane find 3 and a half cans of paint are just enough to paint one third of her room. How many more cans of paint will she need to finish her room and paint a second room of the same size?
|
[
"5",
"17 and a half",
"10",
"12 and a half",
"15"
] |
She will need 7 cans to paint the rest of this room and 10 1/2 for the next room for a total of 17 1/2 cans.
B
The answer is: B
|
B
|
mathematics
|
The county-mandated guidelines at a certain community college specify that for the introductory English class, the professor may choose one of three specified novels, and choose two from a list of 5 specified plays. Thus, the reading list for this introductory class is guaranteed to have one novel and two plays. How many different reading lists could a professor create within these parameters?
|
[
"15",
"30",
"90",
"150",
"360"
] |
There are three possibilities for the novel. With the plays, we are taken a combination of 2 from a set of 5 right n = 5, r = 2, n – r = 3
# of combinations = 5!/2!3! = (5)(4)(3)(2)(1)/(2)(1)(3)(2)(1) = (5)(4)/2 = 10
If the plays are P, Q, R, S, and T, then the 10 sets of two are PQ, PR, PS, PT, QR, QS, QT, RS, RT, & ST.
Any of the three novels can be grouped with any of the 10 possible pairs of plays, for a total of 30 possible reading lists.
Answer: B.
The answer is: B
|
B
|
mathematics
|
In a games hour 4 different types of players came to the ground? cricket 11, hockey 15, football 21, softball 15. In these 4 people play both cricket and hockey, 3people play both softball and football. 6 people play both cricket and football. How many people play only cricket?
|
[
"11",
"1",
"5",
"3",
"9"
] |
people play only cricket = total players in cricket- both cricket and football- both cricket and hockey.
people play only cricket = 11-4-6 = 1
Answer is B
The answer is: B
|
B
|
mathematics
|
The perimeter of a triangle is 20 cm and the inradius of the triangle is 3 cm. What is the area of the triangle?
|
[
"22",
"30",
"77",
"54",
"23"
] |
Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 3 * 20/2
= 30 cm2
Answer:B
The answer is: B
|
B
|
mathematics
|
If the number 98348*0 is exactly divisible by 72, then the minimum value of * is?
|
[
"1",
"2",
"3",
"4",
"5"
] |
72=8*9
divisibility 0f 8 last 3place should be divisible by 8
lly divisibility of 9 sum of digit should be divisible by 9
840 divisible by 8 nd 36 divisible by 9
ANSWER:D
The answer is: D
|
D
|
mathematics
|
Of the science books in a certain supply room, 50 are on botany, 65 are on zoology, 90 are on physics. 50 are on geology, and 110 are on chemistry. If science books are removed randomly from the supply room, how many must be removed to ensure that 80 of the books removed are on the same science?
|
[
"81",
"159",
"166",
"285",
"324"
] |
We can remove 80 books only from physics or from chemistry. Worst case scenario would be if we remove all books on botany, zoology, geology, 79 books on physics and 79 books on chemistry.
We would have 50(botany)+65(zoology)+50(geology)+79(physics)+79(chemistry)=323 books and still won't have 80 books from the same science. As after this, only books on physics and chemistry will be left then any next book would become the 80th book either on physics or on chemistry.
Answer: E.
The answer is: E
|
E
|
mathematics
|
All of the students of Music High School are in the band, the orchestra, or both. 40 percent of the students are in only one group. There are 100 students in the band. If 20 percent of the students are in the band only, how many students are in the orchestra only?
|
[
"30",
"25",
"40",
"55",
"35"
] |
% of students in one group only = 40%
% of students in both groups = 100 - 40 = 60%
% of students in the band only = 20%
Number of students who are in band = 100
60% + 20% = 80% = 100 Students
Finding total students:
x = (100 x 100)/80
x = 125
Students in orchestra only = 125 - 100 = 25
Answer:B
The answer is: B
|
B
|
mathematics
|
#p is defined as 2p+20 for any number p. What is p, if #(#(#p))=-4?
|
[
"–108",
"–44",
"10",
"-18",
"18"
] |
#p = 2p+20 --->#(#p) = 2(2p+20)+20 = 4p+60 and thus #(4p+60) = 2(4p+60)+20 = 8p+140 = -4 ---> 8p= -144 ---> p = -18, D is the correct answer.
The answer is: D
|
D
|
mathematics
|
Company S produces two kinds of stereos: basic and deluxe. Of the stereos produced by Company S last month, 3/4 were basic and the rest were deluxe. If it takes 7/5 as many hours to produce a deluxe stereo as it does to produce a basic stereo, then the number of hours it took to produce the deluxe stereos last month was what fraction of the total number of hours it took to produce all the stereos?
|
[
"6/22",
"5/22",
"7/22",
"4/22",
"3/22"
] |
# of basic stereos was 3/4 of total and # of deluxe stereos was 1/4 of total, let's assume total=16, then Basic=12 and Deluxe=4.
Now, if time needed to produce one Deluxe stereo is 1 unit than time needed to produce one Basic stereo would be 7/5 units. Total time for Basic would be 12*1=12 and total time for Deluxe would be 4*7/5=28/5 --> total time for both of them would be 12+28/5=88/5 --> deluxe/total=28/5 / 88/5= 28/88 =7/22
C
The answer is: C
|
C
|
mathematics
|
-69*39+450=?
|
[
"2736",
"2309",
"-2801",
"-2241",
"None of these"
] |
=> -69*(40-1)+450;
=> -(69*40)+69+450;
=> -2760+519=-2241.
Correct Option: D
The answer is: D
|
D
|
mathematics
|
The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
|
[
"20 kmph",
"40 kmph",
"27 kmph",
"28 kmph",
"22 kmph"
] |
Speed downstream = 60 + 20
= 80 kmph
Speed upstream = 60 - 20
= 40 kmph
Answer:B
The answer is: B
|
B
|
mathematics
|
A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
|
[
"15 hours",
"18 hours",
"20 hours",
"25 hours",
"35 hours"
] |
Let A fill tank in x hrs.
Therefore tank filled in one hrs is 1/x.
And B pipe is twice than A means 2 (1/x).
C pipe is twice than B means 2 (2 (1/x) ) i.e 4/x.
1/x+2/x+4/x = 1/5.
7/x = 1/5.
x = 35 hrs.
ANSWER :e
The answer is: E
|
E
|
mathematics
|
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 5 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
|
[
"23 years",
"24 years",
"25 years",
"26 years",
"27 years"
] |
EXPLANATION
Let the average age of the whole team by x years.
11x – (26 + 21) = 9(x -1)
11x – 9x = 48
2x = 48
x = 24.
So, average age of the team is 24 years.
Answer B
The answer is: B
|
B
|
mathematics
|
The ratio of 2 numbers is 2:8 and their H.C.F. is 40. Their L.C.M. is ?
|
[
"400",
"120",
"80",
"320",
"40"
] |
Let the numbers be 2x and 8x
Their H.C.F. = 40
so the numbers are 2*40 , 8*40 = 80, 320
L.C.M. = 320
Answer is D
The answer is: D
|
D
|
mathematics
|
Calculate the least possible number of vans needed to transport 280 students, given that each van can only take 12 students each?
|
[
"23",
"22",
"21",
"20",
"24"
] |
To find the number of vans, we divide 280 by 12.
280/12 = 23 and remainder = 4
So 23 vans are needed to transport 276 students, and 1 van is needed to transport the 4 remaining students. A total of 24 vans are needed.
correct answer E
The answer is: E
|
E
|
mathematics
|
How many different ways can a group of 8 people be divided into 4 teams of 2 people each?
|
[
"56",
"105",
"75",
"120",
"112"
] |
The required answer is = 8!/(4!*2!*2!*2!*2!) = 105
Answer is B
The answer is: B
|
B
|
mathematics
|
By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 25%?
|
[
"Rs.429",
"Rs.480",
"Rs.429",
"Rs.427",
"Rs.482"
] |
SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.160
SP = CP - Loss = 640 - 160 = Rs.480
Answer:B
The answer is: B
|
B
|
mathematics
|
The price of a VCR is marked at Rs. 12,000. If successive discounts of 15%, 10% and 5% be allowed, then at what price does a customer buy it?
|
[
"Rs. 8400",
"Rs. 8721",
"Rs. 8856",
"Rs. 8956",
"None of these"
] |
Actual price = 95% of 90% of 85% of Rs. 12000
= 95/100 * 90/100 * 85/100 * 12000 = Rs. 8721.
ANSWER:B
The answer is: B
|
B
|
mathematics
|
If log102 = 0.3010, log10 3 = 0.4771, then the number of zeros between the decimal point and the first
significant figure in (0.0432)10 is?
|
[
"10",
"13",
"14",
"15",
"16"
] |
X = (0.0432)10 = (432/10000)10 = (33.24/104)10
Therefore, log10X = 10 (log103 + 4log102-4)
= 10(1.4313 + 1.2040 - 4)
= 10(-1.3647)
= -13.647
= -14.353
Therefore, X = antilog(-14.053)
Thus, number of zeros between the decimal and the first significant figure = 13
ANSWER:B
The answer is: B
|
B
|
mathematics
|
In a group of buffaloes and ducks, the number of legs are 24 more than twice the number of heads. What is the number of buffaloes in the group?
|
[
"12",
"3",
"5",
"8",
"10"
] |
Let the number of buffaloes be x and the number of ducks be y.
Then 4x+2y=2(x+y)+24
=>x=12
ANSWER A 12
The answer is: A
|
A
|
mathematics
|
What is the remainder when the number Y=14^2 * 15^8 is divided by 5?
|
[
"0",
"1",
"2",
"4",
"5"
] |
14^2 has units digit 6
15^8 has units digit 5
Thus Y=14^2*15^8 has units digit 0 and will be divisible by 5. The remainder will be zero
Answer: (A)
The answer is: A
|
A
|
mathematics
|
(166)^2 - (167)^2 =
|
[
"1",
"100",
"229",
"329",
"335"
] |
Using the formula:
(a+1)^2 - a^2 = 2a+1
So, Answer = 167*2 + 1
= 334+1 = 335 = Answer = E
The answer is: E
|
E
|
mathematics
|
In a certain animal population, for each of the first 3 months of life, the probability that an animal will die during that month is 1/10. For a group of 500 newborn members of the population, approximately how many would be expected to survive the first 3 months of life?
|
[
"340",
"346",
"352",
"365",
"370"
] |
Number of newborns that can die in first month = 1/10 * 500 = 50
Survived = 450
Number of newborns that can die in second month = 1/10 * 450 = 45
Survived = 405
Number of newborns that can die in third month = 1/10 * 405 = 40
Survived = 365
Answer:D
The answer is: D
|
D
|
mathematics
|
A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
|
[
"22277",
"29977",
"267676",
"14000",
"18811"
] |
25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
The answer is: D
|
D
|
mathematics
|
A person purchased a TV set for Rs. 2000 and a DVD player for Rs. 2000 . He sold both the items together for Rs. 5000. What percentage of profit did he make?
|
[
"80%",
"80%",
"40%",
"48%",
"25%"
] |
The total CP = Rs. 2000 + Rs. 2000
= Rs. 4000 and SP = Rs. 5000
Profit(%) = (5000 - 4000)/4000 * 100
= 25%
Answer: E
The answer is: E
|
E
|
mathematics
|
If Greg buys 5 shirts, 4 trousers and 2 ties, the total cost is $80. If Greg buys 7 shirts, 4 trousers and 2 ties, the total cost is $70. How much will it cost him to buy 2 trousers, 3 shirts and 1 ties?
|
[
"$37.5",
"$64",
"$75",
"$96",
"Cannot be determined"
] |
Solution: 5x+4y+2z=80 7x+4y+2z=70
adding both the equations= 12x+8y+4z=150
3x+2y+1z=37.5
ans A
The answer is: A
|
A
|
mathematics
|
The sum of the digits of a two-digit number is 15 and the difference between the digits is 3. What is the two-digit number ?
|
[
"69",
"78",
"96",
"Cannot be determined",
"None of these"
] |
Solution
Let the ten's digit be x and unit's digit be y.
Then, x + y = 15 and x = y =3 or y = x = 3.
Solving x + y = 15 and x - y = 3, we get : x = 9, y = 6.
Solving x + y = 15 and y - x = 3, we get : x = 6, y = 9.
So, the number is either 96 or 69. Hence, the number cannot be determined
Answer D
The answer is: D
|
D
|
mathematics
|
What is the leastvalue of x. So that 45x09 is divisible by 3?
|
[
"0",
"5",
"2",
"6",
"7"
] |
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
4 + 5 + x + 0+ 9 = 18 + x
Least value of x may be 0
Therefore 18 + 0= 18 is divisible by 3.
A
The answer is: A
|
A
|
mathematics
|
A batsman makes a score of 74 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
|
[
"25",
"31",
"26",
"29",
"39"
] |
Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 74 = Total runs scored in 17 innings
=> 16(x-3) + 74 = 17x
=> 16x - 48 + 74 = 17x
=> x = 26
Answer is C
The answer is: C
|
C
|
mathematics
|
If 12 men and 16 boys can do a piece of work in 5 days and 13 men together will 24 boys can do it in 4 days. Compare the daily work done by a man with that of a boy.
|
[
"1:1",
"2:1",
"3:1",
"5:1",
"4:1"
] |
B
2:1
12M + 16B ----- 5 days
13M + 24B ------- 4 days
60M + 80B = 52M + 96B
8M = 16B => 1M = 2B
M: B = 2:1
The answer is: B
|
B
|
mathematics
|
45% of major airline companies equip their planes with wireless internet access. 70% of major airlines offer passengers free on-board snacks. What is the greatest possible percentage of major airline companies that offer both wireless internet and free on-board snacks?
|
[
"25%",
"35%",
"45%",
"55%",
"65%"
] |
To maximize the percentage of companies offering both, let's assume that all 45% of companies which offer wireless internet also offer snacks.
The answer is C.
The answer is: C
|
C
|
mathematics
|
The remainder obtained when a prime number greater than 3 is divided by 3 is
|
[
"a) 1 or 3",
"b) 2 or 4",
"c) 3 or 5",
"d) 4 or 5",
"e) 5"
] |
The easiest way to answer this question is probably to pick numbers. Use the next two prime numbers greater than 3, i.e. 7 and 5:
7/3 = 1 + remainder of 4
5/3 = 1 + remainder of 2
This is already sufficient to see that answer choice b) is correct.
B
The answer is: B
|
B
|
mathematics
|
In a certain province in France there are 9 cities. If a single road segment connects only two cities, how many road segments are required in order to connect the cities so that each city is connected to all other cities with a single road segment?
|
[
"36",
"105",
"330",
"14",
"15"
] |
1 city needs 8 roads to connect directly to the rest => 9 city needs 9*8 roads.
One road is counted twice => the number of road needed is 9*8/2 = 36
Answer A
The answer is: A
|
A
|
mathematics
|
If a coin is tossed twice, what is the probability that one of the flips was heads and one of the flips was tails?
|
[
"1/2",
"1/8",
"1/4",
"1/6",
"3/4"
] |
The possible cases are =>{Head,Head} {Head,Tail} {Tail,Head} {Tail,Tail}
Possible Cases=4
Favourable cases = 2
P(E) = 2/4 = 1/2
Answer: A
The answer is: A
|
A
|
mathematics
|
If it takes a machine 2⁄3 minute to produce one item, how many items will it produce in 1 hours?
|
[
"1⁄3",
"4⁄3",
"90",
"120",
"180"
] |
1 item takes 2/3 min so it takes 60 min to produce x
2x/3=60 the x=90
Answer:C
The answer is: C
|
C
|
mathematics
|
If q and r are both odd numbers N, which of the following must also be odd?
|
[
"q – r",
"(q + r)^2",
"q(q + r)",
"(qr)^2",
"q/r"
] |
We're told that q and r are both ODD numbers N. We're asked which of the following must also be odd.
IF...
q = 1
r = 3
Answer A) q – r = 1-3 = -2 NOT odd
Answer B) (q + r)^2 = (1+3)^2 = 16 NOT odd
Answer C) q(q + r) = (1)(4) = 4 NOT odd
Answer D) (qr)^2 = (3)^2 = 9 This IS ODD
Answer E) q/r = 1/3 NOT odd
Final Answer:
D
The answer is: D
|
D
|
mathematics
|
How many four digit numbers have no repeat digits, do not contain zero, and have a sum of digits H equal to 28?
|
[
"14",
"24",
"28",
"48",
"96"
] |
First, look for all 4 digits without repeat that add up to 28. To avoid repetition, start with the highest numbers first.
Start from the largest number possible 9874.
Then the next largest number possible is 9865.
After this, you'll realize no other solution. Clearly the solution needs to start with a 9 (cuz otherwise 8765 is the largest possible, but only equals 26). With a 9, you also need an 8 (cuz otherwise 9765 is the largest possible, but only equals 27). With 98__ only 74 and 65 work.
So you have two solutions. Each can be rearranged in 4!=24 ways. So H=24+24=48.D
The answer is: D
|
D
|
mathematics
|
A certain drive-in movie theater has total of 12 rows of parking spaces. There are 10 parking spaces in the first row and 11 parking spaces each in the next two rows. In each subsequent row there are 2 more parking spaces than in the previous row. What is the total number of parking spaces in the movie theater?
|
[
"219",
"221",
"321",
"192",
"202"
] |
First row 10, Second row 11 and then other 10 rows form an Arithmetic Progression with first term 11 and last term 29 and Avg is 20.
so 20*10+10+11=221
Answer is B
The answer is: B
|
B
|
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