DSQ: Calculating the angle of a sector - GMAT Quantitative
Card 1 of 80
What time is it?
Statement 1: The minute hand and the hour hand are currently forming a 
angle.
Statement 2: The minute hand is on the 6.
What time is it?
Statement 1: The minute hand and the hour hand are currently forming a
Statement 2: The minute hand is on the 6.
Tap to reveal answer
Since there are twelve numbers on the clock, the angular measure from one number to the next is 
; this means 
represents two and a half number positions.
Suppose we know both statements. Since the minute hand is on the 6, the hour hand is either midway between the 3 and the 4, or midway between the 8 and the 9. Both scenarios are possible, as they correspond to 3:30 and 8:30, respectively, so the question is not answered even if we know both statements.
Since there are twelve numbers on the clock, the angular measure from one number to the next is
Suppose we know both statements. Since the minute hand is on the 6, the hour hand is either midway between the 3 and the 4, or midway between the 8 and the 9. Both scenarios are possible, as they correspond to 3:30 and 8:30, respectively, so the question is not answered even if we know both statements.
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What time is it?
Statement 1: The minute hand and the hour hand form a 
angle.
Statement 2: The minute hand is exactly on the 8.
What time is it?
Statement 1: The minute hand and the hour hand form a
Statement 2: The minute hand is exactly on the 8.
Tap to reveal answer
The first event happens numerous times over the course of twelve hours, so the first statement is not enough to deduce the time; all the second statement tells you is that it is forty minutes after an hour (12:40, 1:40, etc.)
Suppose we put the two statements together. It is 
from one number to the next, so the 8:00 position is the 
position. If the hour hand makes a 
with the minute hand, then the hour hand is either at 
or 
. Since forty minutes is two-thirds of an hour, however, the hour hand must be two-thirds of the way from one number to the next.
Case 1: If the hour hand is at 
, then it is at the 
position - in other words, two-thirds of the way from the 5 to the 6. This is consistent with our conditions.
Case 2: If the hour hand is at 
, then it is at the 
position - in other words, one-third of the way from the 10 to the 11. This is inconsistent with our conditions.
Therefore, only the first case is possible, and if we are given both statements, we know it is 5:40.
The first event happens numerous times over the course of twelve hours, so the first statement is not enough to deduce the time; all the second statement tells you is that it is forty minutes after an hour (12:40, 1:40, etc.)
Suppose we put the two statements together. It is
Case 1: If the hour hand is at
Case 2: If the hour hand is at
Therefore, only the first case is possible, and if we are given both statements, we know it is 5:40.
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What time is it?
Statement 1: The minute hand and the hour hand are currently forming a 
angle.
Statement 2: The tip of the minute hand has traveled exactly eight inches since last leaving the 12 position.
What time is it?
Statement 1: The minute hand and the hour hand are currently forming a
Statement 2: The tip of the minute hand has traveled exactly eight inches since last leaving the 12 position.
Tap to reveal answer
The two statements together are not enough unless you know the size of the minute hand; without this information, you cannot tell the angular position of the minute hand, so, even if you know the angle the hands are making, you do not know the position of the hour hand either.
The two statements together are not enough unless you know the size of the minute hand; without this information, you cannot tell the angular position of the minute hand, so, even if you know the angle the hands are making, you do not know the position of the hour hand either.
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Note: Figure NOT drawn to scale.
Refer to the above figure. What is the degree measure of 
?
Statement 1: 
.
Statement 2: 
measures 
.
Note: Figure NOT drawn to scale.
Refer to the above figure. What is the degree measure of
Statement 1:
Statement 2:
Tap to reveal answer
From Statement 1, the measure of the arc can be determined by doubling the measure of the intercepting angle, which is 
. From Statement 2, the measure of the arc can be calculated by subtracting from 
the degree measure of the corresponding major arc, which is 
.
From Statement 1, the measure of the arc can be determined by doubling the measure of the intercepting angle, which is
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After a student body election, Henry is constructing a circle graph to represent the above voter count.
What will be the measure of the central angle of the sector representing Starr (nearest whole number)?
After a student body election, Henry is constructing a circle graph to represent the above voter count.
What will be the measure of the central angle of the sector representing Starr (nearest whole number)?
Tap to reveal answer
The number of people who voted:
245 people voted for Starr, so the sector representing Starr will have measure
The number of people who voted:
245 people voted for Starr, so the sector representing Starr will have measure
← Didn't Know|Knew It →
After a student body election, Henry is constructing a circle graph to represent the above voter count.
What will be the measure of the central angle of the sector representing Thomas (nearest whole number)?
After a student body election, Henry is constructing a circle graph to represent the above voter count.
What will be the measure of the central angle of the sector representing Thomas (nearest whole number)?
Tap to reveal answer
The number of people who voted:
176 people voted for Starr, so the sector representing Starr will have measure
The number of people who voted:
176 people voted for Starr, so the sector representing Starr will have measure
← Didn't Know|Knew It →
Above are the results of the election for student body president that Greg is about to publish in the school newspaper. At the last minute, his friend Melissa stops him and reminds him that there was a sixth candidate, Wilson, who got 202 votes.
Greg's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Douglas decrease (nearest whole degree)?
Above are the results of the election for student body president that Greg is about to publish in the school newspaper. At the last minute, his friend Melissa stops him and reminds him that there was a sixth candidate, Wilson, who got 202 votes.
Greg's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Douglas decrease (nearest whole degree)?
Tap to reveal answer
According to Greg's erroneous information, the number of people who voted was
.
213 voted for Douglas, meaning that his sector will have degree measure
Based on the new information,
people voted.
213 voted for Douglas, meaning that his sector will have degree measure
The reduction in degree measure will be 
.
According to Greg's erroneous information, the number of people who voted was
213 voted for Douglas, meaning that his sector will have degree measure
Based on the new information,
213 voted for Douglas, meaning that his sector will have degree measure
The reduction in degree measure will be
← Didn't Know|Knew It →
Above are the results of the election for student body president that Mike is about to publish in the school newspaper. At the last minute, his friend Veronica stops him and tells him that there was an error in one digit - Lealand got 181 votes, not 101 votes.
Mike's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Lealand increase (nearest whole degree)?
Above are the results of the election for student body president that Mike is about to publish in the school newspaper. At the last minute, his friend Veronica stops him and tells him that there was an error in one digit - Lealand got 181 votes, not 101 votes.
Mike's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Lealand increase (nearest whole degree)?
Tap to reveal answer
According to Mike's erroneous information, the number of people who voted was
,
101 of whom voted for Lealand. Therefore, Mike's initial circle graph would have a sector of degree measure
representing Lealand's share of the vote.
However, the corrected figures are
votes total,
181 of which went to Lealand, so his sector will have measure
,
an increase of 
.
The correct response is 
.
According to Mike's erroneous information, the number of people who voted was
101 of whom voted for Lealand. Therefore, Mike's initial circle graph would have a sector of degree measure
representing Lealand's share of the vote.
However, the corrected figures are
181 of which went to Lealand, so his sector will have measure
an increase of
The correct response is
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Circle A has radius six times that of Circle B; a sector of Circle A with angle measure 
has the same area as Circle B. Evaluate 
.
Circle A has radius six times that of Circle B; a sector of Circle A with angle measure
Tap to reveal answer
Let 
be the radius of Circle B. Then Circle A has radius 
and, subsequently, area 
. Since the area of Circle B is 
, the area of Circle A is 36 times that of Circle B.
The given sector of Circle A has the same area as Circle B, so the sector is one thirty-sixth of the circle. That makes the angle measure of the sector
Let
The given sector of Circle A has the same area as Circle B, so the sector is one thirty-sixth of the circle. That makes the angle measure of the sector
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The radius of Circle A is equal to the sidelength of Square B. A sector of Circle A has the same area as Square B. Which of the following is the degree measure of this sector?
The radius of Circle A is equal to the sidelength of Square B. A sector of Circle A has the same area as Square B. Which of the following is the degree measure of this sector?
Tap to reveal answer
The radius of Circle A and the length of a side of the square are the same - we will call each 
. The area of the circle is 
; that of the square is 
. Therefore, a sector of the circle with area 
will be 
of the circle, which is a sector of measure
The radius of Circle A and the length of a side of the square are the same - we will call each
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What time is it?
Statement 1: The minute hand and the hour hand are currently forming a angle.
Statement 2: The minute hand is on the 6.
What time is it?
Statement 1: The minute hand and the hour hand are currently forming a
Statement 2: The minute hand is on the 6.
Tap to reveal answer
Since there are twelve numbers on the clock, the angular measure from one number to the next is ; this means represents two and a half number positions.
Suppose we know both statements. Since the minute hand is on the 6, the hour hand is either midway between the 3 and the 4, or midway between the 8 and the 9. Both scenarios are possible, as they correspond to 3:30 and 8:30, respectively, so the question is not answered even if we know both statements.
Since there are twelve numbers on the clock, the angular measure from one number to the next is
Suppose we know both statements. Since the minute hand is on the 6, the hour hand is either midway between the 3 and the 4, or midway between the 8 and the 9. Both scenarios are possible, as they correspond to 3:30 and 8:30, respectively, so the question is not answered even if we know both statements.
← Didn't Know|Knew It →
What time is it?
Statement 1: The minute hand and the hour hand form a angle.
Statement 2: The minute hand is exactly on the 8.
What time is it?
Statement 1: The minute hand and the hour hand form a
Statement 2: The minute hand is exactly on the 8.
Tap to reveal answer
The first event happens numerous times over the course of twelve hours, so the first statement is not enough to deduce the time; all the second statement tells you is that it is forty minutes after an hour (12:40, 1:40, etc.)
Suppose we put the two statements together. It is from one number to the next, so the 8:00 position is the position. If the hour hand makes a with the minute hand, then the hour hand is either at or . Since forty minutes is two-thirds of an hour, however, the hour hand must be two-thirds of the way from one number to the next.
Case 1: If the hour hand is at , then it is at the position - in other words, two-thirds of the way from the 5 to the 6. This is consistent with our conditions.
Case 2: If the hour hand is at , then it is at the position - in other words, one-third of the way from the 10 to the 11. This is inconsistent with our conditions.
Therefore, only the first case is possible, and if we are given both statements, we know it is 5:40.
The first event happens numerous times over the course of twelve hours, so the first statement is not enough to deduce the time; all the second statement tells you is that it is forty minutes after an hour (12:40, 1:40, etc.)
Suppose we put the two statements together. It is
Case 1: If the hour hand is at
Case 2: If the hour hand is at
Therefore, only the first case is possible, and if we are given both statements, we know it is 5:40.
← Didn't Know|Knew It →
What time is it?
Statement 1: The minute hand and the hour hand are currently forming a angle.
Statement 2: The tip of the minute hand has traveled exactly eight inches since last leaving the 12 position.
What time is it?
Statement 1: The minute hand and the hour hand are currently forming a
Statement 2: The tip of the minute hand has traveled exactly eight inches since last leaving the 12 position.
Tap to reveal answer
The two statements together are not enough unless you know the size of the minute hand; without this information, you cannot tell the angular position of the minute hand, so, even if you know the angle the hands are making, you do not know the position of the hour hand either.
The two statements together are not enough unless you know the size of the minute hand; without this information, you cannot tell the angular position of the minute hand, so, even if you know the angle the hands are making, you do not know the position of the hour hand either.
← Didn't Know|Knew It →
Note: Figure NOT drawn to scale.
Refer to the above figure. What is the degree measure of ?
Statement 1: .
Statement 2: measures .
Note: Figure NOT drawn to scale.
Refer to the above figure. What is the degree measure of
Statement 1:
Statement 2:
Tap to reveal answer
From Statement 1, the measure of the arc can be determined by doubling the measure of the intercepting angle, which is . From Statement 2, the measure of the arc can be calculated by subtracting from the degree measure of the corresponding major arc, which is .
From Statement 1, the measure of the arc can be determined by doubling the measure of the intercepting angle, which is
← Didn't Know|Knew It →
After a student body election, Henry is constructing a circle graph to represent the above voter count.
What will be the measure of the central angle of the sector representing Starr (nearest whole number)?
After a student body election, Henry is constructing a circle graph to represent the above voter count.
What will be the measure of the central angle of the sector representing Starr (nearest whole number)?
Tap to reveal answer
The number of people who voted:
245 people voted for Starr, so the sector representing Starr will have measure
The number of people who voted:
245 people voted for Starr, so the sector representing Starr will have measure
← Didn't Know|Knew It →
After a student body election, Henry is constructing a circle graph to represent the above voter count.
What will be the measure of the central angle of the sector representing Thomas (nearest whole number)?
After a student body election, Henry is constructing a circle graph to represent the above voter count.
What will be the measure of the central angle of the sector representing Thomas (nearest whole number)?
Tap to reveal answer
The number of people who voted:
176 people voted for Starr, so the sector representing Starr will have measure
The number of people who voted:
176 people voted for Starr, so the sector representing Starr will have measure
← Didn't Know|Knew It →
Above are the results of the election for student body president that Greg is about to publish in the school newspaper. At the last minute, his friend Melissa stops him and reminds him that there was a sixth candidate, Wilson, who got 202 votes.
Greg's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Douglas decrease (nearest whole degree)?
Above are the results of the election for student body president that Greg is about to publish in the school newspaper. At the last minute, his friend Melissa stops him and reminds him that there was a sixth candidate, Wilson, who got 202 votes.
Greg's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Douglas decrease (nearest whole degree)?
Tap to reveal answer
According to Greg's erroneous information, the number of people who voted was
.
213 voted for Douglas, meaning that his sector will have degree measure
Based on the new information,
people voted.
213 voted for Douglas, meaning that his sector will have degree measure
The reduction in degree measure will be .
According to Greg's erroneous information, the number of people who voted was
213 voted for Douglas, meaning that his sector will have degree measure
Based on the new information,
213 voted for Douglas, meaning that his sector will have degree measure
The reduction in degree measure will be
← Didn't Know|Knew It →
Above are the results of the election for student body president that Mike is about to publish in the school newspaper. At the last minute, his friend Veronica stops him and tells him that there was an error in one digit - Lealand got 181 votes, not 101 votes.
Mike's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Lealand increase (nearest whole degree)?
Above are the results of the election for student body president that Mike is about to publish in the school newspaper. At the last minute, his friend Veronica stops him and tells him that there was an error in one digit - Lealand got 181 votes, not 101 votes.
Mike's article includes a circle graph that he will now have to change to reflect this corrected information. By how many degrees will the angle measure of the sector representing Lealand increase (nearest whole degree)?
Tap to reveal answer
According to Mike's erroneous information, the number of people who voted was
,
101 of whom voted for Lealand. Therefore, Mike's initial circle graph would have a sector of degree measure
representing Lealand's share of the vote.
However, the corrected figures are
votes total,
181 of which went to Lealand, so his sector will have measure
,
an increase of .
The correct response is .
According to Mike's erroneous information, the number of people who voted was
101 of whom voted for Lealand. Therefore, Mike's initial circle graph would have a sector of degree measure
representing Lealand's share of the vote.
However, the corrected figures are
181 of which went to Lealand, so his sector will have measure
an increase of
The correct response is
← Didn't Know|Knew It →
Circle A has radius six times that of Circle B; a sector of Circle A with angle measure has the same area as Circle B. Evaluate .
Circle A has radius six times that of Circle B; a sector of Circle A with angle measure
Tap to reveal answer
Let be the radius of Circle B. Then Circle A has radius and, subsequently, area . Since the area of Circle B is , the area of Circle A is 36 times that of Circle B.
The given sector of Circle A has the same area as Circle B, so the sector is one thirty-sixth of the circle. That makes the angle measure of the sector
Let
The given sector of Circle A has the same area as Circle B, so the sector is one thirty-sixth of the circle. That makes the angle measure of the sector
← Didn't Know|Knew It →
The radius of Circle A is equal to the sidelength of Square B. A sector of Circle A has the same area as Square B. Which of the following is the degree measure of this sector?
The radius of Circle A is equal to the sidelength of Square B. A sector of Circle A has the same area as Square B. Which of the following is the degree measure of this sector?
Tap to reveal answer
The radius of Circle A and the length of a side of the square are the same - we will call each . The area of the circle is ; that of the square is . Therefore, a sector of the circle with area will be of the circle, which is a sector of measure
The radius of Circle A and the length of a side of the square are the same - we will call each
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