SAT Math questions 1


Below are some questions to brush your knowledge on the concept of indices, square root and problem solving techniques. Take the test and look at the answer and detailed solutions only when you have tried the questions by yourself at least once.

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SAT Math Practice Test 1

SAT Math Practice Test 2

SAT Algebra Practice Questions

1. What is the number whose 11th part when multiplied with its 5th part gives 2695 as answer?

a)      385

b)      375

c)       395

d)      365

2. I collected some money by raising subscription for opening a library. If the whole amount collected be 1600 currency notes of 100 denomination and each person subscribed as many dollars as there were subscribers, find the amount paid by each subscriber.

a)      250

b)      300

c)       350

d)      400

3. A general wishing to draw up his 2360 men in the form of a solid square found that he had 56 men left over. Find the number of men at the front row.

a)      42

b)      45

c)       48

d)      51

4. If the sum of two numbers is multiplied by each separately, the products so obtained are 2418 and 3666. Find the numbers.

a)      31, 47

b)      32, 48

c)       30, 45

d)      29, 44

5. Find the number whose square is equal to the difference between the squares of 75.15 and 60.12.

a)      43.06

b)      42.90

c)       44.90

d)      45.09

Solutions:

1. Let x be the required number, so that

x/11 * x/5 = 2695
x²                = 11*5*2695
x²                 = 11 * 5 * 5 * 7 * 7 * 11 (factorize 2695)
x²                 = 5² * 7² * 11²
Taking square root on both the sides,

x = 5 * 7 * 11
x = 385

2. Given that the total amount collected = 1600 * 100 = $160,000

Let there be ‘x’ subscribers so that each of them paid $x
Therefore, x² = $160,000

Taking square root on both the sides,
x = 400

3. The number of men who formed the solid square = 2360 – 56 = 2304

Taking square root of 2304, we get 48, which is the number of men in the front row.

4. Let x and y be the two numbers. Then, according to the question,

x (x + y) = 2418
y (x + y) = 3666

Adding the two equations, we get

x (x + y) + y (x + y) = 6084
(x + y) (x + y)       = 6084
(x + y)² = 6084

Taking Square root on both the sides, we get

x + y = 78

As per the question, x = 2418/78 = 31
y = 78-31 = 47

Answer = 31 and 47

5. Let x be the required number, so that

x² = (75.15)² – (60.12)²
x² = (75.15 + 60.12) (75.15 – 60.12)
x² = ( 135.27) (15.03)
x² = 9 * 15.03 * 15.03
x² = 3² * 15.03²

Taking square root on both the sides,

X = 3 * 15.03 = 45.09

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