diff --git a/doc/source/whatsnew/v0.25.0.rst b/doc/source/whatsnew/v0.25.0.rst
index 1fb9b5ae695a0..0f31078d7bf43 100644
--- a/doc/source/whatsnew/v0.25.0.rst
+++ b/doc/source/whatsnew/v0.25.0.rst
@@ -502,7 +502,7 @@ Performance Improvements
 - Improved performance of :meth:`Series.searchsorted`. The speedup is especially large when the dtype is
   int8/int16/int32 and the searched key is within the integer bounds for the dtype (:issue:`22034`)
 - Improved performance of :meth:`pandas.core.groupby.GroupBy.quantile` (:issue:`20405`)
-- Improved performance when slicing :class:`RangeIndex` (:issue:`26565`)
+- Improved performance of slicing and other selected operation on a :class:`RangeIndex` (:issue:`26565`, :issue:`26617`)
 - Improved performance of :meth:`read_csv` by faster tokenizing and faster parsing of small float numbers (:issue:`25784`)
 - Improved performance of :meth:`read_csv` by faster parsing of N/A and boolean values (:issue:`25804`)
 - Improved performance of :attr:`IntervalIndex.is_monotonic`, :attr:`IntervalIndex.is_monotonic_increasing` and :attr:`IntervalIndex.is_monotonic_decreasing` by removing conversion to :class:`MultiIndex` (:issue:`24813`)
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 8538687ca3e91..b8c020ff0edb1 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -4013,11 +4013,7 @@ def __contains__(self, key):
 
     @Appender(_index_shared_docs['contains'] % _index_doc_kwargs)
     def contains(self, key):
-        hash(key)
-        try:
-            return key in self._engine
-        except (TypeError, ValueError):
-            return False
+        return key in self
 
     def __hash__(self):
         raise TypeError("unhashable type: %r" % type(self).__name__)
diff --git a/pandas/core/indexes/range.py b/pandas/core/indexes/range.py
index 82fd7342c027c..14ebc3c7e8e2a 100644
--- a/pandas/core/indexes/range.py
+++ b/pandas/core/indexes/range.py
@@ -1,6 +1,7 @@
 from datetime import timedelta
 import operator
 from sys import getsizeof
+from typing import Union
 import warnings
 
 import numpy as np
@@ -334,6 +335,14 @@ def is_monotonic_decreasing(self):
     def has_duplicates(self):
         return False
 
+    def __contains__(self, key: Union[int, np.integer]) -> bool:
+        hash(key)
+        try:
+            key = ensure_python_int(key)
+        except TypeError:
+            return False
+        return key in self._range
+
     @Appender(_index_shared_docs['get_loc'])
     def get_loc(self, key, method=None, tolerance=None):
         if is_integer(key) and method is None and tolerance is None:
@@ -640,6 +649,12 @@ def __floordiv__(self, other):
                 return self._simple_new(start, start + 1, 1, name=self.name)
         return self._int64index // other
 
+    def all(self) -> bool:
+        return 0 not in self._range
+
+    def any(self) -> bool:
+        return any(self._range)
+
     @classmethod
     def _add_numeric_methods_binary(cls):
         """ add in numeric methods, specialized to RangeIndex """
@@ -725,4 +740,3 @@ def _evaluate_numeric_binop(self, other):
 
 
 RangeIndex._add_numeric_methods()
-RangeIndex._add_logical_methods()
diff --git a/pandas/tests/indexes/test_range.py b/pandas/tests/indexes/test_range.py
index bca50186827de..6eece0ed8efee 100644
--- a/pandas/tests/indexes/test_range.py
+++ b/pandas/tests/indexes/test_range.py
@@ -245,10 +245,9 @@ def test_dtype(self):
         assert self.index.dtype == np.int64
 
     def test_cached_data(self):
-        # GH 26565
-        # Calling RangeIndex._data caches an int64 array of the same length as
-        # self at self._cached_data.
-        # This tests whether _cached_data is being set by various operations.
+        # GH 26565, GH26617
+        # Calling RangeIndex._data caches an int64 array of the same length at
+        # self._cached_data. This test checks whether _cached_data has been set
         idx = RangeIndex(0, 100, 10)
 
         assert idx._cached_data is None
@@ -262,6 +261,24 @@ def test_cached_data(self):
         idx.get_loc(20)
         assert idx._cached_data is None
 
+        90 in idx
+        assert idx._cached_data is None
+
+        91 in idx
+        assert idx._cached_data is None
+
+        idx.contains(90)
+        assert idx._cached_data is None
+
+        idx.contains(91)
+        assert idx._cached_data is None
+
+        idx.all()
+        assert idx._cached_data is None
+
+        idx.any()
+        assert idx._cached_data is None
+
         df = pd.DataFrame({'a': range(10)}, index=idx)
 
         df.loc[50]