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GMAT Sample Questions » GMAT Sample Problem Soving Ability

Quantitative Section : GMAT Sample Problem Solving Ability

Select the correct answer from the given five options by solving the following questions.

1. Out of the two candidates who were standing against each other for the post of an MLA, one of them got 40 % of the total number of vote and the other who won the election got the remaining 60% of all the votes. The defeated candidate got 460 votes less than the number of votes secured by the winner of the election. Find out the total number of votes and the total number of votes gained by the winner of the election.

1. 966, 2300
2. 2300, 966
3. 1380, 2300
4. 2300, 1380
5. None of the above

Explanation:

Suppose the total number of votes = 100

Then, 40% of total number of 100 votes = 40 = number of votes secured by the loser.

And, 60% of total number of 100 votes = 60 = number of votes secured by the winner.

∴ Difference in the votes secured by the two candidates = 60 – 40 = 20.

Hence, we can say that, for total number of votes equal to 100, the difference in the votes earned by the two is equal to 20.

∴ According to the data given in the question, the actual difference of votes between the candidates is = 460

∴ Total number of votes earned by the two candidates = 460*100/20 = 2300

But, we also to find out the number of votes secured by the winner.

It is given that the winner secured 60% of the total number of votes.

∴ 60% of 2300 = 60*2300/100 = 1380

Hence, the correct answer is option d.

2. If a - b = 3 and a2 - b2 = 25, then find the sum of both the variables 'a' and 'b'.

1. 8.6
2. 3.5
3. 2.4
4. 8.33
5. 3.88

Explanation:

We know the standard algebraic formula for (a)2 – (b)2

(a)2 – (b)2 = (a + b) (a – b)

Now, according to the data given in the question, a - b = 3 and a2 - b2 = 25.

Substituting these values in above equation, we get,

25 = (a + b) (3)

∴ (a + b) = 25/3

∴ a + b = 8.3333

Hence, the correct answer is option d.

3. If x + y = 6 and x2 + y2 = 30, then find the product of both the variables 'x' and 'y'.

1. 6
2. 36
3. 2
4. 5
5. 3

Explanation:

We know the standard algebraic formula for (x+y)2

(x+y)2 = x2 + 2xy + y2

Now, according to the data given in the question, x + y = 6 and x2 + y2 = 30

Substituting these values in above equation, we get,

(6)2 = 30 + 2xy

∴ 36 – 30 = 2xy

∴ 6 = 2xy

∴ xy = 3

Hence, the correct answer is option e.

4. If f(x) = 4(x + 2), then what will be the value of f(3)?

1. 20
2. 30
3. 40
4. 10
5. None of the above

Explanation:

According to the data given in the question, f(x) = 4(x + 2)

We have to find out the value of f(3).

∴ Substituting, x = 3 in the equation for f(x), we get,

f(3) = 4(3 + 2)

∴ f(3) = 4(5) = 20

Hence, f(3) = 20

Hence, the correct answer is option a.

5. Find the value of g(2,3) if g(x,y) = x2 + y2/ x+y

1. 12/5
2. 11/12
3. 13/12
4. 5/12
5. 13/5

Explanation:

According to the data given in the question g(x,y) = x2 + y2/ x+y

We have to find the value of the function g(2,3).

Substituting x=2 and y=3 in the given definition of the function 'g', we get,

g(2,3) = (2)2 + (3)2 / (2 + 3)

∴ g(2,3) = (4) + (9)/ (5) = 13/5

Hence, the correct answer is option e.

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GMAT Sample Problem Solving Ability Question Number : 1-5 | 6-10 | 11-15 | 16-20 | 21-25 | 26-30 | 31-35 | 36-40 | 41-45 | 46-50 | 51-55 | 56-60 | 61-65 | 66-70 | 71-75 | 76-80 | 81-85 | 86-90 | 91-95 | 96-100 | 101-105 | 106-110 | 111-115 | 116-120 | 121-125
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