Algebra Practice Test Questions - Quantitative Aptitude -- Free Practice

Question 1

If 5x + y = 15, 5y + z = 25 and 2z + x = 2, what is the value of x ?

A

2✓✗

B

7✓✗

C

9✓✗

D

12✓✗

Explanation

From 5x + y = 15: y = 15 - 5x. From 5y + z = 25: z = 25 - 5y = 25x - 50.
Substituting in 2z + x = 2: 50x - 100 + x = 2, so 51x = 102 and x = 2.

Question 2

Find value of a³ + b³ + 3ab, when value of a+b = 1?

A

1✓✗

B

-1✓✗

C

1/(3ab)✓✗

D

1/(a-b)✓✗

Explanation

a³ + b³ = (a + b)³ - 3ab(a + b) = 1 - 3ab, since a + b = 1.
a³ + b³ + 3ab = 1 - 3ab + 3ab = 1.

Question 3

What will be value of c, if a(a+b+c) = 85; b(a+b+c) = 96; c(a+b+c) = 108?

A

10896✓✗

B

10811✓✗

C

10817✓✗

D

10885✓✗

Explanation

Let S = a + b + c. Adding the three equations: S(a + b + c) = S² = 85 + 96 + 108 = 289, so S = 17.
c × 17 = 108, so c = 10817.

Question 4

If 2x +3y = 30 and (x+y)/y = 118, then find the value of 5y + 6x

A

72✓✗

B

58✓✗

C

64✓✗

D

29✓✗

Explanation

x + yy = 118, so xy + 1 = 118 and xy = 38.
Let x = 3k and y = 8k. 2x + 3y = 6k + 24k = 30k = 30, so k = 1, x = 3 and y = 8.
5y + 6x = 40 + 18 = 58.

Question 5

If x + 4y = 21 and x = -3y, then y =

A

-21✓✗

B

7✓✗

C

21✓✗

D

3✓✗

Explanation

x = -3y, so x + 4y = -3y + 4y = y = 21.
y = 21.

Question 6

P can choose 1 of 2 methods of payment: an annual salary of $35,000 & no commission or annual salary $10,000 & 20% commission on annual sales. What are her annual sales to give her the same pay with either?

A

$100,000✓✗

B

$120,000✓✗

C

$125,000✓✗

D

$130,000✓✗

Explanation

Let the annual sales be S. Both methods give the same pay: 35,000 = 10,000 + 20100S.
20100S = 25,000, so S = $125,000.

Question 7

A man works for 5 days. His pay for each day is 1 12 times that of the previous day. If his total wages are $422 for the 5 days, what was his pay for the second day?

A

$12✓✗

B

$36✓✗

C

$32✓✗

D

$48✓✗

Explanation

Let the first day's pay be a. The pay for the 5 days is a, 1.5a, 2.25a, 3.375a and 5.0625a.
Sum = 13.1875a = 422, so a = 32.
Pay for the second day = 1.5 × 32 = $48.

Question 8

A car dealer sold x used cars and y new cars during May. If the number of used cars sold was 10 greater than the number of new cars sold, which of the following expresses this relationship?

A

x > 10y✓✗

B

x > y +10✓✗

C

x > y -10✓✗

D

x = y +10✓✗

Explanation

The number of used cars x is 10 greater than the number of new cars y, so x = y + 10.

Question 9

T has some money. M gives him 8 cents. F then gives him the same amount as T has at that time. Then G gives him $2.00 & T spends 50 cents. If he has $3.20 left how much did T have to begin with?

A

77 cents✓✗

B

75 cents✓✗

C

15 cents✓✗

D

83 cents✓✗

Explanation

Let T have x cents to begin with. After M gives 8 cents he has x + 8. F gives him the same amount, so he has 2(x + 8).
Then G gives him 200 cents and he spends 50 cents: 2(x + 8) + 200 - 50 = 320.
2(x + 8) = 170, so x + 8 = 85 and x = 77 cents.

Question 10

P said "Give me 3 of your marbles & I will have as many as you." Q said "If you give me 3 of yours, I will have twice as many as you". With how many marbles did P start out?

A

12✓✗

B

15✓✗

C

18✓✗

D

21✓✗

Explanation

Let P have p marbles and Q have q marbles.
P's statement: p + 3 = q - 3, so q = p + 6.
Q's statement: q + 3 = 2(p - 3), so p + 6 + 3 = 2p - 6 and p = 15.
P started with 15 marbles.

Question 11

If 2 + 1/x = 5 - 2/x then x =

A

-1✓✗

B

13✓✗

C

23✓✗

D

1✓✗

Explanation

2 + 1x = 5 - 2x, so 1x + 2x = 3, that is 3x = 3.
x = 1.

Question 12

If a,b and c are non zero numbers and a + b = c, which of the following is equal to 1?

A

(a-b)/c✓✗

B

(a-c)/b✓✗

C

(c-b)/a✓✗

D

(b-a)/c✓✗

Explanation

a + b = c, so c - b = a.
c - ba = aa = 1.

Question 13

If x + 3y = 18 and x/y = 3 then x =

A

-3✓✗

B

3✓✗

C

6✓✗

D

9✓✗

Explanation

xy = 3, so x = 3y.
x + 3y = 18 gives 3y + 3y = 18, so y = 3 and x = 9.

Question 14

M decided to give S $8 for each problem S got correct. S would pay M $5 for each S got wrong. There were 26 problems. After getting the marks, noone paid the other any money. How many problems did S get right?

A

8✓✗

B

13✓✗

C

11✓✗

D

10✓✗

Explanation

Let S get r problems right and w wrong. r + w = 26.
Nobody paid anything, so 8r = 5w. Then 8r = 5(26 - r), so 13r = 130 and r = 10.
S got 10 problems right.

Question 15

The cost of 3 sandwiches, 7 cups of coffee & 4 pieces of cake is $10.20; the cost of 4 sandwiches, 8 cups of coffee & 5 pieces of cake is $12.25. What is the cost of 1 sandwich, 1 coffee & 1 piece of cake?

A

$2.00✓✗

B

$2.05✓✗

C

$2.10✓✗

D

$2.15✓✗

Explanation

Let the costs of a sandwich, a coffee and a cake be s, c and k.
3s + 7c + 4k = 10.20 and 4s + 8c + 5k = 12.25.
Subtracting the first from the second: s + c + k = 12.25 - 10.20 = 2.05.
The cost is $2.05.

Question 16

If n is negative, all EXCEPT which of the following must also be negative?

A

n⁵✓✗

B

n³✓✗

C

1/ n⁵✓✗

D

1/ n²✓✗

Explanation

If n is negative, an odd power of n, n⁵ or n³, is negative, and the reciprocal of a negative number, 1n⁵, is also negative.
But n² is positive, so 1n² is positive. So 1n² is the exception.

Question 17

If x is greater than zero and less than 1, which of the following is the largest?

A

1/ x²✓✗

B

1/x✓✗

C

x✓✗

D

x²✓✗

Explanation

For 0 < x < 1, take x = 0.5: 1x² = 4, 1x = 2, x = 0.5 and x² = 0.25.
Dividing by a smaller positive number gives a larger value, so 1x² is the largest.

Question 18

If 0 < x < 1, which of the following is the largest?

A

x✓✗

B

2x✓✗

C

x²✓✗

D

x + 1✓✗

Explanation

For 0 < x < 1, take x = 0.5: x = 0.5, 2x = 1, x² = 0.25 and x + 1 = 1.5.
x + 1 is greater than 1, whereas x < 1, x² < 1 and 2x < 2. Also x + 1 > 2x because x < 1.
So x + 1 is the largest.

Question 19

X has 10 pairs of socks. If he loses 7 individual socks, what is the greatest number of pairs he can have left?

A

7✓✗

B

6✓✗

C

5✓✗

D

4✓✗

Explanation

X has 10 pairs, that is 20 socks. To keep the greatest number of pairs, the 7 lost socks should come from as few pairs as possible.
7 socks are lost from 4 different pairs (3 pairs entirely and one single sock from the fourth), so 4 pairs are affected.
Pairs left = 10 - 4 = 6.

Question 20

On 31^st May, the sale of candy was $385 m, 7% of total yearly candy sales. Candy sales for the year =

A

$55 m✓✗

B

$550 m✓✗

C

$2695 m✓✗

D

$5500 m✓✗

Explanation

$385 m is 7% of the yearly sales.
Yearly sales = 3857 × 100 = $5500 m.

Question 21

If we divide a two-digit number by the sum of its digits, we get 6 as a quotient and 2 as a remainder. Now if we divide it by the product of its digits, we get 5 as the quotient and 2 as the remainder. What is the number?

A

32✓✗

B

42✓✗

C

63✓✗

D

None of these✓✗

Explanation

Let the number be 10a + b. 10a + b = 6(a + b) + 2, so 4a - 5b = 2.
Also 10a + b = 5ab + 2.
Try a = 3, b = 2: 4 × 3 - 5 × 2 = 2, and 10 × 3 + 2 = 32 = 5 × 6 + 2.
The number is 32.

Question 22

The value of -3-(-10) is how much bigger than the value of -10-(-3) ?

A

0✓✗

B

6✓✗

C

7✓✗

D

14✓✗

Explanation

-3 - (-10) = -3 + 10 = 7 and -10 - (-3) = -10 + 3 = -7.
The difference = 7 - (-7) = 14.

Question 23

10³ + 10⁵ =

A

10⁸✓✗

B

101,000✓✗

C

20⁸✓✗

D

2¹⁵✓✗

Explanation

10³ + 10⁵ = 1000 + 100000 = 101,000.

Question 24

X and Y packed several boxes. If Y packed 60 percent of the total number of boxes, what was the ratio of the number of boxes X packed to the number of boxes Y packed?

A

1 to 6✓✗

B

1 to 4✓✗

C

2 to 3✓✗

D

3 to 5✓✗

Explanation

Y packed 60% of the boxes, so X packed 100 - 60 = 40%.
X : Y = 40 : 60 = 2 : 3.

Question 25

A suit at 40% off is now selling for the reduced price of $144. What was the original price of the suit ?

A

$201.60✓✗

B

$230.40✓✗

C

$240✓✗

D

$360✓✗

Explanation

The suit is 40% off, so the selling price is 60% of the original price.
60% of the original price = $144, so the original price = 14460 × 100 = $240.