DSQ: Understanding decimals - GMAT Quantitative
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is a fraction in lowest terms. Is its decimal representation a terminating decimal or a repeating decimal?
Statement 1: 
is a power of 5.
Statement 2: 
is a multiple of 7.
Statement 1:
Statement 2:
A fraction in lowest terms can be expressed as a terminating decimal if and only if its denominator has no prime factors other than 2 or 5; the numerator is irrelevant. Statement 1 is unhelpful since it only gives information about the numerator. If Statement 2 is assumed - that is, if we know the denominator has 7 as a prime factor - we know that the decimal representation of 
is repeating.
A fraction in lowest terms can be expressed as a terminating decimal if and only if its denominator has no prime factors other than 2 or 5; the numerator is irrelevant. Statement 1 is unhelpful since it only gives information about the numerator. If Statement 2 is assumed - that is, if we know the denominator has 7 as a prime factor - we know that the decimal representation of
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and 
are fractions in lowest terms.
True or false: The result 
can be represented by an integer or a terminating decimal.
Statement 1: Both denominators are even.
Statement 2: Both denominators are multiples of 3.
True or false: The result
Statement 1: Both denominators are even.
Statement 2: Both denominators are multiples of 3.
Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:
In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.
Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:
In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.
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and 
are fractions in lowest terms.
True or false: The result 
can be represented by an integer or a terminating decimal.
Statement 1: Neither denominator is a multiple of 5.
Statement 2: Both denominators are powers of 2.
True or false: The result
Statement 1: Neither denominator is a multiple of 5.
Statement 2: Both denominators are powers of 2.
Assume Statement 1 alone. Examine these two examples:
Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.
Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.
Assume Statement 1 alone. Examine these two examples:
Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.
Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.
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and 
are fractions in lowest terms.
True or false: The result 
can be represented by an integer or a terminating decimal.
Statement 1: The denominator of 
is a power of 7.
Statement 2: The denominator of 
is a power of 3.
True or false: The result
Statement 1: The denominator of
Statement 2: The denominator of
Assume both statements. Examine these two examples; both fit the main condition and those given in both statements.
In only one case is the product equivalent to an integer or a terminating decimal.
Assume both statements. Examine these two examples; both fit the main condition and those given in both statements.
In only one case is the product equivalent to an integer or a terminating decimal.
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and 
are fractions in lowest terms.
True or false: The result 
can be represented by an integer or a terminating decimal.
Statement 1: The denominator of 
is three times the numerator of 
.
Statement 2: The denominator of 
is six times the numerator of 
.
True or false: The result
Statement 1: The denominator of
Statement 2: The denominator of
Assume Statement 1 alone. Rewrite the fractions as follows:
, where 
- that is, their lowest-terms representations.
By Statement 1, 
, so 
. Therefore,
Since 
is in lowest terms, 
is not a multiple of 3, so the 3 must remain in the denominator, even if the 
and the 
can be reduced. Since a fraction which, in lowest terms, has a denominator with any prime factor other than 2 or 5 cannot be represented by an integer or a terminating decimal, Statement 1 proves that 
has a repeating decimal as its equivalent.
A similar argument can be used to demonstrate that Statement 2 proves the same of 
.
Assume Statement 1 alone. Rewrite the fractions as follows:
By Statement 1,
Since
A similar argument can be used to demonstrate that Statement 2 proves the same of
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and 
are fractions in lowest terms.
True or false: The result 
can be represented by an integer or a terminating decimal.
Statement 1: The denominator of 
is five times the numerator of 
.
Statement 2: The denominator of 
is eight times the numerator of 
.
True or false: The result
Statement 1: The denominator of
Statement 2: The denominator of
Assume Statement 1 alone. Examine these examples:
In both cases, the main conditon and that of Statement 1 are satisfied, but in only one case can the result be represented by a terminating decimal or integer.
A similar argument shows Statement 2 alone to be insufficient:
Assume both statements. Then rewrite the fractions as follows:
, where 
- that is, their lowest-terms representations.
By Statement 1, 
; by Statement 2, 
. Therefore,
,
and their product is
,
a terminating decimal.
Assume Statement 1 alone. Examine these examples:
In both cases, the main conditon and that of Statement 1 are satisfied, but in only one case can the result be represented by a terminating decimal or integer.
A similar argument shows Statement 2 alone to be insufficient:
Assume both statements. Then rewrite the fractions as follows:
By Statement 1,
and their product is
a terminating decimal.
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and 
are fractions in lowest terms.
True or false: The result 
can be represented by an integer or a terminating decimal.
Statement 1: Both fractions have powers of 5 in their denominators.
Statement 2: Both fractions have powers of 3 in their numerators.
True or false: The result
Statement 1: Both fractions have powers of 5 in their denominators.
Statement 2: Both fractions have powers of 3 in their numerators.
Assume Statement 1 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. Statement 1 says this about both fractions; the sum of terminating decimals is itself an integer or a terminating decimal.
Statement 2 alone provides insuffiicient information. Examine these examples:
Both fit the conditions of the main premise and Statement 2, but in only one case is the sum equal to a terminating decimal.
Assume Statement 1 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. Statement 1 says this about both fractions; the sum of terminating decimals is itself an integer or a terminating decimal.
Statement 2 alone provides insuffiicient information. Examine these examples:
Both fit the conditions of the main premise and Statement 2, but in only one case is the sum equal to a terminating decimal.
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Solve for 
in the following equation.
I) 
is equivalent to seventy nine hundredths.
II) The slope of the line parallel to this equation is 
.
Solve for
I)
II) The slope of the line parallel to this equation is
We have one equation and two unknowns. To find x, we need to find y.
I) Tells us that y is .79 therefore we can plug this value into our equation and solve for x.
Plugging in the y value from Statement I and using algebraic operations to solve for x.
Multiply first term.
Subtract 4.74 from both sides.
Divide by -13.
II) Is irrelevant.
Therefore Statement I) alone is sufficient to answer the question but Statement II) alone is not.
We have one equation and two unknowns. To find x, we need to find y.
I) Tells us that y is .79 therefore we can plug this value into our equation and solve for x.
Plugging in the y value from Statement I and using algebraic operations to solve for x.
Multiply first term.
Subtract 4.74 from both sides.
Divide by -13.
II) Is irrelevant.
Therefore Statement I) alone is sufficient to answer the question but Statement II) alone is not.
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is a fraction in lowest terms. Is its decimal representation a terminating decimal or a repeating decimal?
Statement 1: is a power of 5.
Statement 2: is a multiple of 7.
Statement 1:
Statement 2:
A fraction in lowest terms can be expressed as a terminating decimal if and only if its denominator has no prime factors other than 2 or 5; the numerator is irrelevant. Statement 1 is unhelpful since it only gives information about the numerator. If Statement 2 is assumed - that is, if we know the denominator has 7 as a prime factor - we know that the decimal representation of is repeating.
A fraction in lowest terms can be expressed as a terminating decimal if and only if its denominator has no prime factors other than 2 or 5; the numerator is irrelevant. Statement 1 is unhelpful since it only gives information about the numerator. If Statement 2 is assumed - that is, if we know the denominator has 7 as a prime factor - we know that the decimal representation of
Compare your answer with the correct one above
and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: Both denominators are even.
Statement 2: Both denominators are multiples of 3.
True or false: The result
Statement 1: Both denominators are even.
Statement 2: Both denominators are multiples of 3.
Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:
In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.
Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:
In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.
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and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: Neither denominator is a multiple of 5.
Statement 2: Both denominators are powers of 2.
True or false: The result
Statement 1: Neither denominator is a multiple of 5.
Statement 2: Both denominators are powers of 2.
Assume Statement 1 alone. Examine these two examples:
Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.
Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.
Assume Statement 1 alone. Examine these two examples:
Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.
Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.
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and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: The denominator of is a power of 7.
Statement 2: The denominator of is a power of 3.
True or false: The result
Statement 1: The denominator of
Statement 2: The denominator of
Assume both statements. Examine these two examples; both fit the main condition and those given in both statements.
In only one case is the product equivalent to an integer or a terminating decimal.
Assume both statements. Examine these two examples; both fit the main condition and those given in both statements.
In only one case is the product equivalent to an integer or a terminating decimal.
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and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: The denominator of is three times the numerator of .
Statement 2: The denominator of is six times the numerator of .
True or false: The result
Statement 1: The denominator of
Statement 2: The denominator of
Assume Statement 1 alone. Rewrite the fractions as follows:
, where - that is, their lowest-terms representations.
By Statement 1, , so . Therefore,
Since is in lowest terms, is not a multiple of 3, so the 3 must remain in the denominator, even if the and the can be reduced. Since a fraction which, in lowest terms, has a denominator with any prime factor other than 2 or 5 cannot be represented by an integer or a terminating decimal, Statement 1 proves that has a repeating decimal as its equivalent.
A similar argument can be used to demonstrate that Statement 2 proves the same of .
Assume Statement 1 alone. Rewrite the fractions as follows:
By Statement 1,
Since
A similar argument can be used to demonstrate that Statement 2 proves the same of
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and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: The denominator of is five times the numerator of .
Statement 2: The denominator of is eight times the numerator of .
True or false: The result
Statement 1: The denominator of
Statement 2: The denominator of
Assume Statement 1 alone. Examine these examples:
In both cases, the main conditon and that of Statement 1 are satisfied, but in only one case can the result be represented by a terminating decimal or integer.
A similar argument shows Statement 2 alone to be insufficient:
Assume both statements. Then rewrite the fractions as follows:
, where - that is, their lowest-terms representations.
By Statement 1, ; by Statement 2, . Therefore,
,
and their product is
,
a terminating decimal.
Assume Statement 1 alone. Examine these examples:
In both cases, the main conditon and that of Statement 1 are satisfied, but in only one case can the result be represented by a terminating decimal or integer.
A similar argument shows Statement 2 alone to be insufficient:
Assume both statements. Then rewrite the fractions as follows:
By Statement 1,
and their product is
a terminating decimal.
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and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: Both fractions have powers of 5 in their denominators.
Statement 2: Both fractions have powers of 3 in their numerators.
True or false: The result
Statement 1: Both fractions have powers of 5 in their denominators.
Statement 2: Both fractions have powers of 3 in their numerators.
Assume Statement 1 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. Statement 1 says this about both fractions; the sum of terminating decimals is itself an integer or a terminating decimal.
Statement 2 alone provides insuffiicient information. Examine these examples:
Both fit the conditions of the main premise and Statement 2, but in only one case is the sum equal to a terminating decimal.
Assume Statement 1 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. Statement 1 says this about both fractions; the sum of terminating decimals is itself an integer or a terminating decimal.
Statement 2 alone provides insuffiicient information. Examine these examples:
Both fit the conditions of the main premise and Statement 2, but in only one case is the sum equal to a terminating decimal.
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Solve for in the following equation.
I) is equivalent to seventy nine hundredths.
II) The slope of the line parallel to this equation is .
Solve for
I)
II) The slope of the line parallel to this equation is
We have one equation and two unknowns. To find x, we need to find y.
I) Tells us that y is .79 therefore we can plug this value into our equation and solve for x.
Plugging in the y value from Statement I and using algebraic operations to solve for x.
Multiply first term.
Subtract 4.74 from both sides.
Divide by -13.
II) Is irrelevant.
Therefore Statement I) alone is sufficient to answer the question but Statement II) alone is not.
We have one equation and two unknowns. To find x, we need to find y.
I) Tells us that y is .79 therefore we can plug this value into our equation and solve for x.
Plugging in the y value from Statement I and using algebraic operations to solve for x.
Multiply first term.
Subtract 4.74 from both sides.
Divide by -13.
II) Is irrelevant.
Therefore Statement I) alone is sufficient to answer the question but Statement II) alone is not.
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is a fraction in lowest terms. Is its decimal representation a terminating decimal or a repeating decimal?
Statement 1: is a power of 5.
Statement 2: is a multiple of 7.
Statement 1:
Statement 2:
A fraction in lowest terms can be expressed as a terminating decimal if and only if its denominator has no prime factors other than 2 or 5; the numerator is irrelevant. Statement 1 is unhelpful since it only gives information about the numerator. If Statement 2 is assumed - that is, if we know the denominator has 7 as a prime factor - we know that the decimal representation of is repeating.
A fraction in lowest terms can be expressed as a terminating decimal if and only if its denominator has no prime factors other than 2 or 5; the numerator is irrelevant. Statement 1 is unhelpful since it only gives information about the numerator. If Statement 2 is assumed - that is, if we know the denominator has 7 as a prime factor - we know that the decimal representation of
Compare your answer with the correct one above
and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: Both denominators are even.
Statement 2: Both denominators are multiples of 3.
True or false: The result
Statement 1: Both denominators are even.
Statement 2: Both denominators are multiples of 3.
Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:
In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.
Assume both statements to be true. A multiple of both 2 and 3 is also a multiple of 6, so both denominators are multiples of 6. Examine these two examples:
In both examples, the conditions of the problem, including both statements, are met, but in only one is the sum equivalent to a terminating decimal or integer.
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and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: Neither denominator is a multiple of 5.
Statement 2: Both denominators are powers of 2.
True or false: The result
Statement 1: Neither denominator is a multiple of 5.
Statement 2: Both denominators are powers of 2.
Assume Statement 1 alone. Examine these two examples:
Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.
Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.
Assume Statement 1 alone. Examine these two examples:
Both fit the main condition and that of Statement 1, but in only one case is the sum equal to a terminating decimal or integer.
Assume Statement 2 alone. A necessary and sufficient condition for a lowest-terms fraction to be equivalent to a terminating decimal is that its only prime factors are 2 and 5. By Statement 2, both denominators have 2 as their only prime factor, so both can be represented by terminating decimals; their product must be terminating as well.
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and are fractions in lowest terms.
True or false: The result can be represented by an integer or a terminating decimal.
Statement 1: The denominator of is a power of 7.
Statement 2: The denominator of is a power of 3.
True or false: The result
Statement 1: The denominator of
Statement 2: The denominator of
Assume both statements. Examine these two examples; both fit the main condition and those given in both statements.
In only one case is the product equivalent to an integer or a terminating decimal.
Assume both statements. Examine these two examples; both fit the main condition and those given in both statements.
In only one case is the product equivalent to an integer or a terminating decimal.
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