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GMAT QUANTITATIVE REASONING LINEAR EQUATIONS DATA SUFFICIENCY Diagnostic Test
GMAT QUANTITATIVE REASONING
LINEAR EQUATIONS
DATA SUFFICIENCY
Diagnostic Test
Question
A shop sells lubricants in 50-litre and 10-litre containers. If the
total volume of lubricants sold by the shop in a day was 280
litres, how many 10-litre containers did the shop sell in the day?
Statement 1: The shop sold less than ten 10-litre containers on
that day.
Statement 2: The shop sold more than three 50-litre containers
on that day.
Step 1
Get clarity on when the data is sufficient
How many 10-litre containers did the shop sell?We will not even look at the statements while answering the following questions
When is the data sufficient and when not?
How many 10-litre containers did the shop sell?We will not even look at the statements while answering the following questions
When is the data sufficient and when not?
The data is sufficient if we can determine
uniquely the number of 10-litre
containers sold by the shop.
How many 10-litre containers did the shop sell?We will not even look at the statements while answering the following questions
When is the data sufficient and when not?
The data is sufficient if we can determine
uniquely the number of 10-litre
containers sold by the shop.
If the information in the statement(s)
results in more than one value for the
number of 10-litre containers sold, data
is NOT sufficient.
How many 10-litre containers did the shop sell?We will not even look at the statements while answering the following questions
When is the data sufficient and when not? What is the approach?
The data is sufficient if we can determine
uniquely the number of 10-litre
containers sold by the shop.
If the information in the statement(s)
results in more than one value for the
number of 10-litre containers sold, data
is NOT sufficient.
How many 10-litre containers did the shop sell?We will not even look at the statements while answering the following questions
When is the data sufficient and when not? What is the approach?
The data is sufficient if we can determine
uniquely the number of 10-litre
containers sold by the shop.
If the information in the statement(s)
results in more than one value for the
number of 10-litre containers sold, data
is NOT sufficient.
Look for a counter example for the data given.
How many 10-litre containers did the shop sell?We will not even look at the statements while answering the following questions
When is the data sufficient and when not? What is the approach?
The data is sufficient if we can determine
uniquely the number of 10-litre
containers sold by the shop.
If the information in the statement(s)
results in more than one value for the
number of 10-litre containers sold, data
is NOT sufficient.
Look for a counter example for the data given.
If we are able to find two values for the
number of 10-litre containers sold while
satisfying the condition in the statement, data
is NOT sufficient.
How many 10-litre containers did the shop sell?We will not even look at the statements while answering the following questions
When is the data sufficient and when not? What is the approach?
The data is sufficient if we can determine
uniquely the number of 10-litre
containers sold by the shop.
If the information in the statement(s)
results in more than one value for the
number of 10-litre containers sold, data
is NOT sufficient.
Look for a counter example for the data given.
If we are able to find two values for the
number of 10-litre containers sold while
satisfying the condition in the statement, data
is NOT sufficient.
If only one value is possible, the data is
SUFFICIENT.
Step 2
Let’s evaluate statement 1 alone
Statement 1: The shop sold less than ten 10-litre containers on that day.
How many 10-litre containers did the shop sell?
01 Look for more than one value that satisfies statement 1
Statement 1: The shop sold less than ten 10-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
01 Look for more than one value that satisfies statement 1
Statement 1: The shop sold less than ten 10-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers.
01 Look for more than one value that satisfies statement 1
Statement 1: The shop sold less than ten 10-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
01 Look for more than one value that satisfies statement 1
Statement 1: The shop sold less than ten 10-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
01 Look for more than one value that satisfies statement 1
Statement 1: The shop sold less than ten 10-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value using statement 1 alone.
We are not able to determine the value uniquely.
01 Look for more than one value that satisfies statement 1
Statement 1: The shop sold less than ten 10-litre containers on that day.
Statement 1 alone is NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value using statement 1 alone.
We are not able to determine the value uniquely.
01 Look for more than one value that satisfies statement 1
Statement 1: The shop sold less than ten 10-litre containers on that day.
Eliminate choices A and D.Statement 1 alone is NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value using statement 1 alone.
We are not able to determine the value uniquely.
01 Look for more than one value that satisfies statement 1
Statement 1: The shop sold less than ten 10-litre containers on that day.
Choices narrow down to B, C or E.
Eliminate choices A and D.Statement 1 alone is NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value using statement 1 alone.
We are not able to determine the value uniquely.
01 Look for more than one value that satisfies statement 1
Step 3
Let’s evaluate statement 2 alone.
Statement 2: The shop sold more than three 50-litre containers on that day.
How many 10-litre containers did the shop sell?
02 Look for more than one value that satisfies statement 2
Statement 2: The shop sold more than three 50-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
02 Look for more than one value that satisfies statement 2
Statement 2: The shop sold more than three 50-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold more than three 50-litre containers.
02 Look for more than one value that satisfies statement 2
Statement 2: The shop sold more than three 50-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
02 Look for more than one value that satisfies statement 2
Statement 2: The shop sold more than three 50-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
02 Look for more than one value that satisfies statement 2
Statement 2: The shop sold more than three 50-litre containers on that day.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value using statement 2 alone.
We are not able to determine the value uniquely.
02 Look for more than one value that satisfies statement 2
Statement 2: The shop sold more than three 50-litre containers on that day.
Statement 2 alone is NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value using statement 2 alone.
We are not able to determine the value uniquely.
02 Look for more than one value that satisfies statement 2
Statement 2: The shop sold more than three 50-litre containers on that day.
Statement 2 alone is NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value using statement 2 alone.
We are not able to determine the value uniquely.
02 Look for more than one value that satisfies statement 2
Eliminate choice B.
Statement 2: The shop sold more than three 50-litre containers on that day.
Statement 2 alone is NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value using statement 2 alone.
We are not able to determine the value uniquely.
02 Look for more than one value that satisfies statement 2
Choices narrow down to C or E.
Eliminate choice B.
Step 4
Let’s combine data from both the
statements.
Statements Together : 10-litre containers < 10; 50-litre containers > 3
How many 10-litre containers did the shop sell?
03 Look for more than one value that satisfies both statements
Statements Together : 10-litre containers < 10; 50-litre containers > 3
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
03 Look for more than one value that satisfies both statements
Statements Together : 10-litre containers < 10; 50-litre containers > 3
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers
and more than three 50-litre containers.
03 Look for more than one value that satisfies both statements
Statements Together : 10-litre containers < 10; 50-litre containers > 3
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers
and more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
03 Look for more than one value that satisfies both statements
Statements Together : 10-litre containers < 10; 50-litre containers > 3
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers
and more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
03 Look for more than one value that satisfies both statements
Statements Together : 10-litre containers < 10; 50-litre containers > 3
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers
and more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value even after combining both statements.
We are not able to determine the value uniquely.
03 Look for more than one value that satisfies both statements
Statements Together : 10-litre containers < 10; 50-litre containers > 3
Statements together NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers
and more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value even after combining both statements.
We are not able to determine the value uniquely.
03 Look for more than one value that satisfies both statements
Statements Together : 10-litre containers < 10; 50-litre containers > 3
Statements together NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers
and more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value even after combining both statements.
We are not able to determine the value uniquely.
03 Look for more than one value that satisfies both statements
Eliminate choice C.
Statements Together : 10-litre containers < 10; 50-litre containers > 3
Statements together NOT sufficient.
How many 10-litre containers did the shop sell?
Total volume sold = 280 litres.
The shop sold less than ten 10-litre containers
and more than three 50-litre containers.
Possibility 1: Five 50-litre containers and
three 10-litre containers.
Possibility 2: Four 50-litre containers and
eight 10-litre containers.
We get more than one value even after combining both statements.
We are not able to determine the value uniquely.
03 Look for more than one value that satisfies both statements
Answer is choice E.
Eliminate choice C.
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