1003083302
Level:
C
Let \( a \) and \( c \) be positive numbers. A number \( b \) equals \( 96\% \) of the number \( 2a + b \) and \( 64\% \) of the number \( 5a + c \). It means that
\( c=70a \).
\( c=1.5a \).
\( c=14a \).
\( c=48a \).
Percent problems
1003083301
Level:
C
If a number \( 3b \) is by \( 20\% \) bigger than half of the number \( 2a + b \), then the number \( a \) is bigger than \( b \) by
\( 100\% \).
\( 80\% \).
\( 50\% \).
\( 200\% \).
1003082209
Level:
B
Two circles are given. The radius of the first circle is by \( 30\% \) longer than the radius of the other circle. It means that the area of the first circle is bigger than the area of the second one
by more than \( 60\% \).
by less than \( 50\% \), but more than \( 40\% \).
by less than \( 60\% \), but more than \( 50\% \).
by exactly \( 60\% \).
1003082208
Level:
B
Find a positive number whose square is by \( 500\% \) greater than this number.
\( 6 \)
\( 5 \)
\( 7 \)
\( 8 \)
1003082207
Level:
B
The angle \( \beta \) is by \( 25\% \) less than the angle \( \gamma \) and by \( 50\% \) greater than the angle \( \alpha \). The angle \( \gamma \) is
by \( 100\% \) greater than \( \alpha \).
by \( 50\% \) greater than \( \alpha \).
by \( 75\% \) greater than \( \alpha \).
by \( 25\% \) greater than \( \alpha \).
1003082206
Level:
B
The price of the book was increased by \( 4.5 \) złotys which is \( 15\% \) of the initial price. Then it was increased by another \( 1.5 \) złotys. By how many percent did the overall price of the book increase?
by \( 20\% \)
by \( 6 \) złotys
by \( 25\% \)
by \( 16\% \)
1003082205
Level:
B
One side of a rectangle was increased by \( 10\% \). By how many percent has the area of the rectangle changed?
it has increased by \( 10\% \)
it has decreased by \( 10\% \)
it has increased by \( 20\% \)
it has decreased by \( 20\% \)
1003082204
Level:
B
By how many percent should we lengthen the edge of a cube so that its surface area is increased by \( 21\% \)?
by \( 10\% \)
by \( 21\% \)
by \( 11\% \)
by \( 42\% \)
1003082203
Level:
B
\( 30\% \) of some goods were sold with a \( 15\% \) profit and the remaining amount was sold with a \( 10\% \) profit. What was the overall profit from the sale?
\( 11.5\% \)
\( 12.5\% \)
\( 25\% \)
\( 12\% \)
1003082202
Level:
B
If \( 20\% \) of the number \( 55 \) is by \( 4 \) smaller than \( 30\% \) of the number \( x \), then:
\( x=50 \)
\( x=75 \)
\( x=45 \)
\( x=33 \)