Embed Size (px)
Citation preview
GMAT QUANTITATIVE REASONING
WORD PROBLEMS
ALGEBRA: FACTORIZING
PROBLEM SOLVING
Diagnostic Test
Question
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation. The difference between the number of sheep in the first row of the farms is 4 and the difference in the number of sheep in the two farms is 152. What is the sum of the number of sheep in the two farms?A. 620B. 730C. 441D. 289E. 480
Step 1
Express what is stated in words into
equations or expressions
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation.
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation.
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation.
What is the sum of the number of sheep in the two farms?
01 Sheep made to stand in square formation
Step 1: Words to equations
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation.
What is the sum of the number of sheep in the two farms?
01 Sheep made to stand in square formation
In a square formation, the number of sheep in a row is the same as the number of rows.
Step 1: Words to equations
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation.
What is the sum of the number of sheep in the two farms?
01 Sheep made to stand in square formation
In a square formation, the number of sheep in a row is the same as the number of rows.
Let there be ‘a’ rows in farm A. So, there will ‘a’ sheep in each row of farm A.
Step 1: Words to equations
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation.
What is the sum of the number of sheep in the two farms?
01 Sheep made to stand in square formation
In a square formation, the number of sheep in a row is the same as the number of rows.
Let there be ‘a’ rows in farm A. So, there will ‘a’ sheep in each row of farm A.
Therefore, total number of sheep in farm A = a * a = a2
Step 1: Words to equations
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation.
What is the sum of the number of sheep in the two farms?
01 Sheep made to stand in square formation
In a square formation, the number of sheep in a row is the same as the number of rows.
Let there be ‘a’ rows in farm A. So, there will ‘a’ sheep in each row of farm A.
Therefore, total number of sheep in farm A = a * a = a2
Let there be ‘b’ rows in farm B. So, there will ‘b’ sheep in each row of farm B.
Step 1: Words to equations
Sheep in farm A are made to stand in a square formation; sheep in farm B are made to stand in another square formation.
What is the sum of the number of sheep in the two farms?
01 Sheep made to stand in square formation
In a square formation, the number of sheep in a row is the same as the number of rows.
Let there be ‘a’ rows in farm A. So, there will ‘a’ sheep in each row of farm A.
Therefore, total number of sheep in farm A = a * a = a2
Let there be ‘b’ rows in farm B. So, there will ‘b’ sheep in each row of farm B.
Therefore, total number of sheep in farm B = b * b = b2
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
02 First row difference is 4
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
02 First row difference is 4
Number of sheep in first row of farm A = a
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
02 First row difference is 4
Number of sheep in first row of farm A = a
Number of sheep in first row of farm B = b
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
02 First row difference is 4
Number of sheep in first row of farm A = a
Number of sheep in first row of farm B = b
Difference = (a – b) = 4
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
02 First row difference is 4 03 Difference in number of sheep is 152
Number of sheep in first row of farm A = a
Number of sheep in first row of farm B = b
Difference = (a – b) = 4
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
02 First row difference is 4 03 Difference in number of sheep is 152
Number of sheep in first row of farm A = a
Number of sheep in first row of farm B = b
Difference = (a – b) = 4
Number of sheep in farm A = a2
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
02 First row difference is 4 03 Difference in number of sheep is 152
Number of sheep in first row of farm A = a
Number of sheep in first row of farm B = b
Difference = (a – b) = 4
Number of sheep in farm A = a2
Number of sheep in farm B = b2
The difference between the number of sheep in the first row of the farms is 4 the difference in the number of sheep in the two
farms is 152
What is the sum of the number of sheep in the two farms?
Step 1: Words to equations continued…
02 First row difference is 4 03 Difference in number of sheep is 152
Number of sheep in first row of farm A = a
Number of sheep in first row of farm B = b
Difference = (a – b) = 4
Number of sheep in farm A = a2
Number of sheep in farm B = b2
Difference in number of sheep is(a2 – b2) = 152
Step 2
Algebraic Factorization to determine
a and b
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
a2 – b2 = 152 … eqn (1)
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
a2 – b2 = 152 … eqn (1)
a – b = 4 … eqn (2)
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
a2 – b2 = 152 … eqn (1)
a – b = 4 … eqn (2)
i.e., 152 = (a + b) * 4
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
a2 – b2 = 152 … eqn (1)
a – b = 4 … eqn (2)
i.e., 152 = (a + b) * 4
Or (a + b) =152
4= 38 … eqn (3)
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
a2 – b2 = 152 … eqn (1)
a – b = 4 … eqn (2)
i.e., 152 = (a + b) * 4
Or (a + b) =152
4= 38 … eqn (3)
Solve equations (2) and (3) to get ‘a’ and ‘b’
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
a2 – b2 = 152 … eqn (1)
a – b = 4 … eqn (2)
i.e., 152 = (a + b) * 4
Or (a + b) =152
4= 38 … eqn (3)
Solve equations (2) and (3) to get ‘a’ and ‘b’
Adding (2) and (3), (a – b + a + b) = 4 + 38Or 2a = 42. a = 21
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
a2 – b2 = 152 … eqn (1)
a – b = 4 … eqn (2)
i.e., 152 = (a + b) * 4
Or (a + b) =152
4= 38 … eqn (3)
Solve equations (2) and (3) to get ‘a’ and ‘b’
Adding (2) and (3), (a – b + a + b) = 4 + 38Or 2a = 42. a = 21
If a = 21, in eqn (2) 21 – b = 4. So, b = 17
Finding a and b is not the last step. There is one more to go.
What is the sum of the number of sheep in the two farms?a – b =4 and a2 – b2 = 152
Step 2: Factorize to determine ‘a’ and ‘b’
a2 – b2 = (a + b)(a – b)
a2 – b2 = 152 … eqn (1)
a – b = 4 … eqn (2)
i.e., 152 = (a + b) * 4
Or (a + b) =152
4= 38 … eqn (3)
Solve equations (2) and (3) to get ‘a’ and ‘b’
Adding (2) and (3), (a – b + a + b) = 4 + 38Or 2a = 42. a = 21
If a = 21, in eqn (2) 21 – b = 4. So, b = 17
Step 3
Compute the total number of sheep in
the two farms
What is the sum of the number of sheep in the two farms?a =21 and b = 17
What is the sum of the number of sheep in the two farms?a =21 and b = 17
Step 3: Compute the total number of sheep
What is the sum of the number of sheep in the two farms?a =21 and b = 17
Step 3: Compute the total number of sheep
Total number of sheep in farm A = a2 = 212 = 441
What is the sum of the number of sheep in the two farms?a =21 and b = 17
Step 3: Compute the total number of sheep
Total number of sheep in farm A = a2 = 212 = 441
Total number of sheep in farm B = b2 = 172 = 289
What is the sum of the number of sheep in the two farms?a =21 and b = 17
Step 3: Compute the total number of sheep
Total number of sheep in farm A = a2 = 212 = 441
Total number of sheep in farm B = b2 = 172 = 289
Total number of sheep in both the farms together = 441 + 289 = 730
What is the sum of the number of sheep in the two farms?a =21 and b = 17
Step 3: Compute the total number of sheep
Total number of sheep in farm A = a2 = 212 = 441
Total number of sheep in farm B = b2 = 172 = 289
Total number of sheep in both the farms together = 441 + 289 = 730
730 sheep in both farms
What is the sum of the number of sheep in the two farms?a =21 and b = 17
Step 3: Compute the total number of sheep
Total number of sheep in farm A = a2 = 212 = 441
Total number of sheep in farm B = b2 = 172 = 289
Total number of sheep in both the farms together = 441 + 289 = 730
Choices B is the answer.
730 sheep in both farms
For more questions
Visit http://www.4gmat.com
GMAT Classes and GMAT Preparation
Send your comments / feedback to
4GMATWe offer classroom training in Chennai and Bangalore
Tutors include GMAT 98%ilers, US B School graduates and IIM graduates
Call us: +91 95000 48484
Mail us: [email protected]
